Criticizing the police in a superhero story is kind of straightforward, examples exist, but what about the military in a kaiju story? Like, it's one thing to have the monster be immune to weapons but how do you avoid the usual cliches?
I would say most kaiju movies are pretty critical of the military - and so are a lot of Western giant monsters movies, to a lesser extent. The military is almost always impotent at best in a kaiju movie, rarely accomplishing anything more than stalling for time, and often end up making the situation worse. All the military's actions in the original Godzilla, for example, do nothing but make the monster more pissed off, until his final and most horrible rampage is directly provoked by the military's incredibly thorough and diverse attempt to kill him with every weapon they can think of. That is not a flattering portrayal of the military.
In fact, this trope is so common in the kaiju genre that it wasn't until decades after its inception that people tried to go against it - one of the directors of the 90's Godzilla movies talked about how G-Force in those movies was made because he always felt annoyed as a child that the military never accomplished much, and wanted to have them put up a better fight. Yet even then, MechaGodzilla, Moguera, and the various super xs never win - they come close, but Godzilla proves indomitable in the end.
Victories in kaiju movies overwhelmingly hinge on noncombatants and diplomacy - the happy ending comes from a scientist creating an ingenious invention, or fairies convincing their moth goddess to save our ass, or simply allowing Godzilla to swim off into the sunset when he's done defending his territory from the invasive monster of the week.
Some modern American kaiju pastiches find interesting ways to make the military useful while trying to stick to the themes baked into the genre's bones - Godzilla 2014 has a protagonist who, while in the military, specifically works as a bomb disposal expert, i.e. someone who keeps violence from escalating rather than perpetuate. Said character is drawn as a direct reflection of Godzilla himself in the same movie - heroes defined by their desire to stop a violent situation from exploding rather to destroy for the sake of destroying.
Pacific Rim explicitly focuses on a military organization of pilots in giant robots trying to fend off alien invaders using kaiju as weapons - but in the movie's greatest break from reality, said force is woefully underfunded, stripped to just a handful of robots and pilots. While the Jaegers of Pacific Rim have the trappings of some real world miltiary stuff, I think ultimately they don't resemble the military that much in execution, being more akin to, like, a remnant of an army turned into a guerilla resistance force, and really they make more sense when you take them as a metaphor for the few people actively fighting against climate change in our world (which the movie makes pretty clear is basically the theme, more or less - the aliens are specifically seeking our world out because we've fucked up the environment enough to make it favorable to them). And, ultimately, the Jaegers only manage to get their job done thanks to the help of two very brave scientists.
But, in all honestly, I feel no need to do away with the "cliche" of the impotent military in kaiju flicks. Fuck the military. Show them as incompetent, war-mongering, overfunded and undereffective assholes. Fuck 'em. They get their cocks sucked by every other genre with a budget, they can take a few beatings in the kaiju flicks.
I misspoke--it's less the "cliche" of the impotent military and more the usual criticisms that come up whenever you don't show them in the most propaganda flavored light possible. You get people complaining how two dimensional your evil general was, for example.
