Well, remember, many totalitarian regimes are in fact woefully inefficient. Largely because the emperor/fuhrer/first citizen needs to make sure the people beneath him are either not ambitious enough or competent enough to potentially overthrow them. The emperor has to be a paranoid backstabber to maintain a totalitarian regime, and he thus assumes everyone else is a paranoid backstabber. Hence members of his cabinet are constantly rotating, no united vision can get done, the empire needs multiple spy organisations that are all spying on each other and murdering each other, et cetera, et cetera.

Basically, an incompetent totalitarian regime shouldn't be hard to write; real-life totalitarian regimes tend to be woefully incompetent as is.

I don't think "mind boggling" stupidity will be plausible, otherwise, why weren't they overthrown decades ago? Just because nobody thought of it? That's not a good enough reason for an oppressive regime that rules a large number of people; there is always some percentage of any country that hates the government (even our own here in the USA).

What a totalitarian regime can be is mind-bogglingly wasteful of gold and lives, and mind-bogglingly cruel to dissenters and even innocents they think are dissenters. They can be mind-bogglingly adamant on religious adherence, even if the leaders themselves are not and partake of drugs, sexual orgies, liquor, and rock-and-roll with abandon -- religion keeps the subjects in check and gives them something to worry about. A totalitarian regime, even if not very competent in actual battle, is typically very good at the psychopathy of scaring the shit out of their subjects to keep them in line.

Due to that fright, your rebels may find themselves unable to trust anyone, betrayed by the very citizens they are trying to free, informed upon, spied upon, and in real danger because if they are caught, they are publicly and slowly skinned alive and tortured to create the maximum screaming pain possible, just as an example. And don't think most of the citizens will be outraged by this, most of them will be cowed.

I would make your antagonists (like the British fighting the American Colonists) not exactly incompetent, but wasteful of men, stuck in traditional battle, and unable to adapt to guerrilla tactics, hit-and-run ambush (i.e. the rebels kill a few and then run like hell), subterfuge (roadside bombs / traps, or similar lethal traps in woods), supply line disruption, and so on.

I would not make this fight between competent fighters and incompetent fighters; I would make between highly intelligent fighters and normally competent fighters. The regime doesn't stumble. The rebels keep outsmarting them.

Because the rebel leaders are smart, and to them the regime is predictable, and anything predictable can be exploited.

People can be intelligent and competent yet still unable to do their job. The military might be underfunded (seems really unlikely but you can set your story up however you like). You might be the best commander in history but you are going to fail if your equipment and personnel are not at the levels that they should be.

Or maybe people get promoted in this inactive military for political reasons. Usually a higher ranking soldier gets that way due to experience and training. But if there is no chance at experience and the training is okay but done by people who also lack that experience, coming through the ranks doesn't equal competence at your job.

If the Empire has money though, look for a lot of these problems to be fixed pretty quickly. You can't improve infrastructure overnight, and distributing tech and getting personnel up to speed will take time too. But staffing levels and training are going to go way up in weeks after the first attack or two.

Alternatively, am I approaching this from the wrong direction, and
need to have the Empire represent legitimate antagonistic force?

You've got plenty of answers here so I'll offer a different approach.

The "real" tension in the story, and where most of the conflict will arise, is between the rebel leaders themselves.

Develop the Anti-Team first

I think you should focus on subverting the Team Trope before you make a decision about the Evil Empire trope.

What is an Anti-Team? Rather than heroes learning to work together and synergizing through their strengths to defeat the big bad, you have competitive egos trying to occupy the same leadership roles, not listening to each other, and making selfish mistakes. How does that get resolved? Does it resolve?

I've looked for "anti-team" stories (for my own use) and haven't found many satisfying examples.

• 
  Mystery Men starts off anti-team. They are all jealous and hyper-critical of each other's hero personas. They become the rag-tag team of misfits by the end. By overcoming their anti-team tendencies they become true heroes.


• 
  Guardians of the Galaxy is a team of anti-heroes – each individual has anti-social traits but there's no question they are a team, just dysfunctional.


• 
  Farscape combines anti-heroes with anti-team – the show suffers from lack of focus (bordering on experimental theater). Everyone is equally unlikeable. There is no heart. "Heart" is an archetype on the team – usually the girl – who de-fuses interpersonal conflicts and holds the team together with niceness. I'm not sure if this is a flaw with anti-team or a flaw of Farscape.


• 
  The Last Jedi shows traditional heroes fail because they are anti-team. They leave on personal wild goose chases, they mutiny against their superiors, they misjudge their enemies (and friends), they are over-confident, and when facing loss they make empty gestures of self-sacrifice.

Some other examples come close but don't quite fit. Watchmen is a broken team (arguably not even a team, more like damaged alumni). Star Trek's mirror universe would presumably function as anti-team but it exists for narrative counterpoint. Mirror universe doesn't make sense but neither do the Sith.

Which brings us to...

Rebel against what?

With a fractious and uncertain Anti-Team carrying most of the drama and interest, ditch the cartoon villains. Assuming you have shades of grey and moral ambiguities within the good guys, you don't need a vantablack counterpoint because your team isn't milk white – you can still use the antagonist to counterpoint something – there has to be a pretext for the anti-team to come together. But if their enemy is satanic skullspiders wearing swastika helmets and their plan is to murder the universe, the anti-team are always going to have congruent strategies. Moreover, why are they the only ones rebelling if everyone routinely gets steamrolled?

Empires are not just marching boots they are also economies and cultures. This is the issue I have with Star Wars. A "flat" antagonist isn't doing you any narrative favors, there's nothing to divide your team. That's why I say work out the dynamics of the anti-team first. Figure out what you want to say with that dynamic because the antagonist will be the thing that makes it worse, and succeeds in counterpoint.

Trope Talk does a good breakdown of problems with Evil Empires, as related to goals of the protagonist (ie: replace the Emperor).
https://www.youtube.com/watch?v=FCBIXgYCds4

Consider real life rebellions.

If the rebellion is religious, like an English King abolishes the Catholic church and then dies leaving his daughters to sort it out, your rebels might have history with Rome, or prefer a weak local church that can be bribed. They don't all need to be devout crusaders against a cartoon monotrope, some interests overlap but some don't. The US South rebelled so they could keep their colonial economy and lifestyle, but the clock was ticking as they'd lost power in Congress. Meanwhile there were Confederate states that didn't export cotton, and some Union states had race riots. The conflict can still be about a broad thing, but leave room for fractures to occur where some rebels aren't invested in every aspect of the cause.

the Anti-Evil Empire

To break the trope of the Evil Empire, I suggest:

• 
  There is no Evil Empire Don Quixote is a bizarre comedy about a man who is rebelling against the loss of chivalry (or something). He misidentifies his targets, mistakes locals for his enemies, and is a general crazy nuisance. He attacks windmills believing they are monsters. Terry Guiliam's Brazil can be interpreted similarly where the "attacks" are provoked by bucking the system.


• 
  The Empire isn't Evil and is actually very disappointed that you would feel that way considering everything it's done to ensure universal happiness. (Brave New World, Fahrenheit 451)


• 
  The Empire didn't know it was evil but now that you have uncovered this dark secret you will be eliminated.


• 
  The Empire is Evil but (fill in the blank)

I like this idea. It's a fresh take on an old trope, and could be very effective. I could see essentially two directions to go on this:

• The Empire is Irrelevant: This largely sounds like the direction you're already going. The plot mainly takes place between the groups of protagonists. In this case, I don't think either the characters or the readers need to know the Empire is incompetent. If they find out, they should do it naturally --a raid is surprisingly successful, resistance is minimal, minions seem eager to change sides. However, in order to keep the audience from feeling cheated, you'll really need to keep the internal tensions high. Depending on whether you're going for adventure story or tragedy, the end of the book will either be that the heroes finally overcome their differences and subsequently find it comparatively easy to overcome the Empire, or that they defeat themselves, and the Empire endures without ever even noticing the rebels exist.




• Satire: This could either be a broad or a bleak comedy. Incompetent comic antagonists are nothing new. If you're going for the funny, you'll essentially be writing Spaceballs. If it's a bleak comedy, then it's more or less the tragic version of "The Empire is Irrelevant," except this time, we see in excruciating detail, just how ineffective the Empire actually is, and how that still doesn't make any difference --the political satire version of No Exit.

Talented individuals can be seen as dangerous to totalitarian regimes. Stalin executed many very capable generals and when the crisis came, talented, experienced officers were in short supply and rather nervous.

Removing potential threats and rivals could possibly thin out the acknowledged talent within the regime. Some of your brilliant minds were smart enough to not push the fact of their intelligence - the smartest one in the room needs to be smart enough to let someone with more power think themselves more intelligent.

If the regime you envision is pulling in different directions simultaneously, they destroy themselves and one of the brilliant minds would realize this and recommend that a single plan with contingency plans be adopted and followed to defeat the threat.

People will quarrel and pull in opposite directions, sabotage each other and do all manner of self destructive things, but give them a common foe and that falls aside. Defeat of the rebellion is more important than egos and rivals can be disposed of later - that is what peace is for - politics.

What you have are talented theorists who never had the opportunity to actually see their plans in action with no resistance to the regime. Their predecessor probably retired as did his, the last one to have seen ‘active service’ might have told stories to his heirs before dying of old age.

They must agree on defeating the revolution, methods might differ but various theories would be employed, some might be rather odd, the brainchild of the guy who graduated last in his class.

Surprise or disbelief could lead to early errors, but those would diminish as the more intelligent among them discuss strategy and let the others know ‘adults are talking - be quiet kids’ while they figure a way to crush the rebels.

The regime has the advantage of numbers, intel, discipline and training. The rebels must be more motivated and mobile as they will rely on blending in with the population and being as hard to identify as possible lest they be captured and end up being executed in a rather graphic way.

Take a look at this article about the military in Arabic countries. The main point (at risk of overgeneralising) is that the biggest risk to an Arab leader is their own military. Hence they practice "divide and rule" by preventing different branches of the military from working together (no combined operations), and work to systematically eliminate initiative at all levels, including senior ranks.

You might also take a look at the Ottoman Empire, where inheritance went to brothers before sons, leading to a situation where the brothers of the ruler would either be killed or kept isolated in a gilded cage. The latter often meant that when the sultan died his heir would be pulled out of his pleasure palace and stuck on the throne with absolutely no idea of current events or how to rule.

I hate to say it, but you can always blame religion. The mindless, illogical stupidity that could result from centuries of supernatural doctrine is boundless. I mean, imagine if the Aztecs had never existed and somebody made them up.

Guerrilla warfare

The key to winning an rebellion is surprise. The rebels must appear out of nowhere, attack before the defenders can get organized and leave before reinforcements arrive.

This is standard guerrilla tactics, and is very hard to defend against. Even otherwise competent empires can struggle. The empire's basic dilemma is that they need to defend everywhere, while the rebels only have to attack in one place. Suddenly there are a thousand rebels facing a dozen guards. The guards will fail without having to be incompetent.

Transports are good guerrilla targets. Transports of food, money and arms are all better off in the hands of the rebels than the empire, don't you think?

Of course, the empire know this and will guard the transports. But there are many transports and the roads are long. The guards will get bored and the ambush happens where and when they least expect it.

To make it work, the rebels need spies. They need to know guard numbers, transport schedules and so on. If citizens are mostly in favour of the rebels, this will be easy.

One point of conflict between rebel leaders will be sharing this information.

Unfortunately, guerrilla warfare is only the start, to actually win, the rebels need to take and hold territory. This is much harder. The rebels should weaken the empire a lot before starting this.

Another point of conflict will be when to start the open war.

Some of the rebels will basically be bandits, in it for the loot. Others will be trying to free the oppressed people from tyranny. These groups are not going to like each other.

I can think of three distinct approaches, though they're not mutually exclusive. From most to least specific:

1 - Fail/win narrowly, but spectacularly

The evil empire doesn't just have overwhelming numbers, it has all the flashy symbols of power associated with a wealthy and well established military. Oversized, overengineered siege machines that can devastate entire cities - as long as the flanks and supply lines hold. Elite cavalry units in shining armor, straight from the capital, with twenty years of experience - in the one terrain type they're familiar with.

In short, give your antagonist a Death Star or two, show the reader its power when used correctly, then go for the exhaust port. Victory for your rebels is not a foregone conclusion. They need a plan, and they need to execute it well. But when they do, it really costs the empire, and might provoke an even greater show of force - to save face perhaps, or because for any smaller scale dissent, it is a proven tactic.

This helps retain suspense because any slip-up will cost the rebellion dearly, and places emphasis on the rebel leaders having to work together well to pull off their plans.

2 - It's not about if you win, it's about how

The antagonist, attempting to defend a large territory, is higly reactive and tends to respond with targeted, but excessive measures, while the protagonists always stay one step ahead. The rebels exploit one weakness, the empire overcompensates, they strike somewhere else.

The intent here is to require the protagonists to come up with a new strategy or approach for every major battle. They can't ever reach a stable consensus because the tactic they used last time won't likely work again. If a given weakness can only be exploited once, what goals should they prioritize? Which strategy will win the war and wich one will just extend it?

Murder mysteries work that way. It's expected that the case will be solved and the murderer arrested, the question is who did it? How? And why did they do it?

3 - Rather than an antagonist, think of the empire as a force of nature

As long as the rebels keep winning, the fight against the dangerous-but-predictable empire becomes more of a man vs nature conflict that can, over time, shift into the background or escalate depending on the needs of the story. Compare to the zombie genre, where casualties are usually the result of bad planning, infighting or resource shortages rather than the zombies outsmarting anyone. In world and story building, you should focus on how the empire/the war restricts the protagonists, which unique challenges it poses and how different approaches to these challenges play out. Season to taste with interpersonal conflicts.

An alternative solution: don't make the Empire make mistakes, make all the mistakes in the past.
This historically has led to defeat and includes:

1. Badly resourced armies thanks to corruption


2. Mass desertions of conscripts


3. Key figures in the chain of command switching allegiance.

The last can give some tension as they'll likely want less change than the original rebels, and the original rebels could easily feel like the newcomers are hijacking their rebellion.

The British Empire in the first World War can provide some good reference material for you. Officers usually came from the Aristocracy, and so the chain of command was stratified according to class instead of competency.

You can contrast the Canadian Army from the same period which did not have the same class structure at the societal level which allowed for more flexibility with their military. An interesting guy to research is Arthur Currie (https://en.wikipedia.org/wiki/Arthur_Currie).

One idea is that the rebels might be better at something than the Empire is. Think Prussian artillery in the Franco-Prussian war, Napoleon's logistics vs his opponents, even the American war of independence.

What is interesting about the American war of independence was that it was a rebellion that ended up beating the British Empire in pitched battles. There are probably a lot of ideas to mined from that era, including a fractious rebellion where the various factions had opposing interests as well as common ones (i.e. independence from the Empire).

There are a lot of examples in history that cover pretty much the exact idea that you have put forth here.

A couple more ideas for research for you:
The Romans vs the Picts
Gallic Wars (Romans again against various Gallic tribes)
Ottoman Empire has a number of examples. The Battle of Lepanto is a good one where a variety of city states and powers came together to defeat the Ottomans. The Arab Revolt (WWI) is another similar episode. At Gallipoli the Ottomans successfully held off an invasion of British and Anzac forces.

Hope this helps.

1: They're fighting it from the outside, perhaps somebody/somebodies are fighting it from the inside. Used poorly this can destroy any sense of jeopardy, but then.. so can most tools.

2: Systemic failures, depend on context to find relevance. Corruption in the supply chain, soldiers & police selling off their equipment to gangs, the issues here really depend on how the Empire would deal with these sorts of issues should they occur...

If it's contemporary/scifi the government surveillance & communication channels could be routinely compromised.

3: Too little too late - The Empire can improve at those things your rebellion exploits, or at least try alternative solutions to fill the gaps in policy exposed. Your heroes are supposed to be clever, and cleverness isn't well-shown by being able to exploit the same holes in readiness over and over. Look at any extant organisation and you'll find some aspect they are trying to improve in the way they operate..and therefore you'll find a translatable trend.

If there is enough of a cultural divide/dislocation in this empire to provide grounds for an effective rebellion (as opposed to coup d'etat) it is likely that the administration of the empire is largely in the hands of those born, raised and/or indoctrinated into viewing the empire as at least 'the lesser of many evils' and that culture, as the empire, is failing & decadent. It's just not plausible for a culture to 'turn around' in a few years, so one can build intrinsic attitudes into positions of authority that allow exploitation.

Of course, it's important to keep those agents of the empire personal if they're to have any impact or value (imo) and not have them all reading off exactly the same script.

Many authors choose the approach that the evil was after all necessary, or at least an expedient way to a necessary end.

eg Brian McLellan's Powder Mage

early antagonists 'the Privileged' were asshats, but asshats trying to prevent the end of the world that noone else knew about.

Revolutions are fought by rich folks against other rich folks using poor folks, even most fictional ones are led by some long lost prince or other.

What this means is that the Empire may have it's focus on area's other than the Rebellion. The American Revolutionary War for example was preceded by many other conflicts that the British Empire was involved in, which whilst it generally came out on top, had their own costs. Rich Colonials decided they should not have to help pay for the costs of keeping themselves securely linked to european trade & produce and if anybody should tax and govern the residents of the 13 colonies, it should be them, so a Rebellion formed.

In asymmetric warfare, indeed sensibly in any kind of warfare, one naturally chooses means & objectives according to one's strengths and the opponents weaknesses. For this rebellion to succeed finally, and for your heroes to be demonstrably omgamazing, the rebellion need not succeed in every project, nor the empire fail in all of it's.

The Rebel knows they are a rebel and know what the Empire is and what it is not, they know the tools of the Empire because they are a part of it, but the Empire does not know the tools of the Rebel because it is not a part of them. The Empire will end up fighting shadows because any dissident group, any act of competence could be deliberately undermining it. It will self-harm and direct it's resources against things other than the rebellion itself.

It will seek to stave off rebel sympathies by way of reasoned argument or fear or coercion or bread & circuses not knowing that none of these matter because the author has chosen his side.

This while the rebel heroes have laser focus.

There are already many ways of how a "Stupid Empire" could react or manifest and how the rebels could exploit that.

So I would like to add a few tools of how to SHOW and EXPLAIN the stupidity, so that the reader can understand and relate to that fact.
This way you can better avoid unfulfilling "Ex-Machina" feelings.

Just pick what matches your story best.

1. 
   Have a competent but underpowered imperial Officer
   
   He knows about what goes wrong and why. But he has not enough power to make much of a difference.
   He could be the main antagonist and the "face" of the Empire (to your readers that is) and either argues with his superiors or can even be too afraid to do that.
   
   Bonus point: If the rebel infighting gets too destructive and you need to ease imperial pressure, you can just kill him off (being sent to an unholdable position for example). Or you make him more powerful (getting promoted) if you need a real bossfight at the end.
   
   
   
   


2. 
   Have a very overconfident and very powerful imperial Officer
   
   You can also do the opposite of the above.
   Having one or two severly flawed but powerful characters in the empire could help you show that much of the stupidity is not in fact systemic but rather personal.
   
   This is not mutually exclusive to 1.
   
   
   
   


3. 
   Have a mole (or multiple)
   
   If the rebels can deliver false intelligence to the Empire, it will be clear, why they make wrong decisions all the time. Just make it clear to the reader that there is a very effective mole. (But don't overuse this. A mole's info can't deviate too far from the truth or he will be found out).
   
   Bonus point: If you need to crank up the pressure, let the mole be found and imperial decisions suddenly get better.
   
   (Just a little addition: It could be kinda hilarious if every rebel fraction has their own moles but they are too paranoid to tell each other. In the end they find out that they already had control over most of the imperial command structure but never knew... and now the emperor caught all of them.)
   
   
   
   


4. 
   Have strong propaganda
   
   If your Empire broadcasts a strong message of "We are invincible", even imperial officers will believe that and underestimate the threat of an actual rebellion.
   But only showing the propaganda itself will not do. You need to make clear that the Empires decisions are based on propaganda beliefs.
   
   Bonus point: With time and experience the officers will learn to be more cautious or aggressive. So you can again crank the pressure up over time.
   
   Or make leading officers get more and more demoralized if you wish. (The thought of everyone - rebels AND empire spiralling into chaos is quite intriguing I think).
   
   
   
   


5. 
   Have a knowledgebal informant in your rebellion
   
   Having someone like an imperial Ex-Officer who can explain how the Empire reacts is a good way of making mistakes relatable.
   Just make him an important part of planning or briefings.
   
   Or have him explain things to inexperienced rebel grunts who scoff at the empires stupidity.
   
   
   
   


6. 
   Have an outside viewer
   
   Someone like a traveler or a normal civilian, having to flee because rebels took his hometown for example, is a good tool to show how the Empire reacts and how their priorities are set (and how the rebels themselves are perceived by the population).
   
   He could either get to a refugee camp or just flee across the country.
   
   To spice this up you could make him a rebellion-deserter who really has reasons to run from the rebels.
   
   
   
   


7. 
   Have good - maybe honorful - reasons for wrong priorities
   
   How about an Empire that makes an effort to protect civilians? But they constantly underestimate the trouble of managing refugee camps and evacuations (and yes the Empire can be evil and still care about its workforce. No one said they would provide good care in these camps... just some protection. Eg: If I want to get more gold in the future, I need some gold miners).
   
   A brawl in a refugee camp for example might very well throw them off guard.
   The rebels could even abuse this tactic to lower the empires ability to react.
   
   Or they are very cautious and really don't want to battle unprepared so they wait just a little too long for supplies.