The Charlton Heston version; I was not aware of yet another re-make and a check of IMDb leads me to believe I didn’t miss much – a kick boxing star? 
Except any good apocalypse has a significant decrease in population, so “overcrowding” isn’t usually a problem.
There are some good ones in books. “Slow Apocalypse” by John Varley could almost be the Trope Namer. It’s not a dystopia as you describe, it’s the current day world dealing with something that kills a lot of people, but not in a big sudden nuclear war kind of way. Things just gradually fall apart a bit more every day.
Worse - Will Smith. I Am Legend is a remake of Omega Man.
Technically, it’s an adaptation of the same-named novel. The third try, of which only Vincent Price came closest to the actual plot of the novel. No film yet “gets” it, and Will Smith’s version actually turned the last line/title on its head, completely missing the point.
And none of the three fit this thread. They are all post-apocalyptic.
For dark comedy, there is Idiocracy:
My impression is that the OP is looking for more like “pre-apocalypse”. Like nuclear war or a population collapse hasn’t happened yet.
Then let me suggest CNN Nightly News. 
Not a movie, but I think The Leftovers TV series hits a lot of these elements. The physical world is unaffected, but everyone’s understandably freaked out and will be for decades to come. But people need to go on with their lives. I find this sort of thing more nuanced and interesting than the more doomy approaches.
I think I get it: In a dystopia, the world is very different, because someone or someones wanted it to be very different, and worked hard to make that happen. In the movies that the OP wants, though, people, including the people in power, want to keep things as normal as they can, but are only partly succeeding, because something very bad has happened out of their control.
Is that it?
Comedy? Wait… wasn’t that a documentary?
It’s been a long time but I think that counts.
Would ‘Idiocracy’ count or would it be considered too post apocalyptic?
The An Orison of Sonmi 451 part of Cloud Atlas certainly fits the bill. It’s the 22nd century, and pollution, radiation, and climate change have transformed large areas into “deadlands”, and the deadlands are growing every year, with refugees fleeing to habitable areas and those who aren’t so lucky dying off or reverting to primitive societies. South Korea is one of the last few places with a functioning government, but it’s not exactly a great place to live - the entire country is run by corporations, with trademarks replacing everyday words because those companies have become monopolies (all movies are “disneys”, all coffee is “starbuck”, all cars are “fords”, etc.), and all the menial jobs are performed by clones that are property of the corporation that grows them and which are eventually euthanized and processed into food before they can get old enough to start developing reason and free will.
It’s pretty clear that nothing is going to get better, and a later segment of the movie/book shows that it didn’t.
Oh, every Dopers favorite book, which has been adapted to a film trilogy, fit this theme. May I introduce you to the pleasures of:
Atlas Shrugged
?
Rocky Horror Picture show audience: “YOU MAY NOT!”
Technically more of a shantytown, Mortville in “Desperate Living” definitely qualified for:
The place probably could have used a bomb.
That’s an interesting case.
They have a more or less functioning society at the start of the movie. So it isn’t post apocalyptic except maybe in the strictest sense by comparing it to present day (I certainly wouldn’t want to live there, but most people seem to be doing fine.)
But it is obvious that by the next year there will be massive famine. I’m expecting 90% death rate, mostly because the populous is too stupid to remember there are other sources of food than vending machines. So it does fit the thread, like a dark comedy version of Soylent Green.
There’s also the Dystopias where the flaws are only apparent outside the system like Brave New World or the Twilight Zone episode “Number 12 Looks Just Like You”
I kind of feel like you missed the point there. They were already suffering from crop failures and dust bowls and the like, which is why they were desperate enough to listen to the Smartest Man in the World in the first place (Cite: President Camacho). Since he figured out how to get at least some crops to start growing again, there’s at least some hope for the future.
Sure, maybe the overall inertia of society and all the stupid people might make things still fail, but it’s not a certainly.