These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Critical Research Failure: The stupid lower classes out-breeding the intelligent upper class and ruining everything by flooding the world with their stupidity is a very old idea. It's also not at all true.
In the Japanese dub of the film, Toshihiko Seki voices Joe. The hilarity came with the fact he previously voiced Rau Le Creuset, another character who wants to do more or less the same plan Joe does in the film, except that implies exterminate the whole human race. He also voiced Rey Za Burrel, who works with someone who has a less-extreme version of Creuset's plans. This also reachs another layer of hilarity if you know about the Destiny Plan, except in this movie, it's completely goes the opposite way intended and it's self-inflicted rather than imposed by some Big Bad.
Hype Backlash: Many people make comparisons to this film for everything they see as a "dumb" societal trend, such as the continued popularity of Michael Bay movies. This scares some people away by making the movie seem very preachy and Anvilicious when it's really just a goofy, high-concept comedy running on Rule of Funny. In other words, it's a slapstick comedy that's only loved by pretentious eltists, because it appeals to their sense of pretension at a base level - the "stupid" satire isn't as deep as they believe, as the stupid jokes really are stupid jokes.
"Ah, you talk like a fag, and your shit's all retarded."
MST3K Mantra: Apparently, there are people who watched this movie and thought it was being as serious as Red Dawn, which, as we all know, was a documentary.
Same goes for people nitpicking about how it would take longer to get the electrolytes out of the soil, how come people can still ride motorcycles/play guitars/etc.
In the case of the guitars, this is what the Army is now teaching in Basic training. Note all of the band is in matching camoflauge, and is supposed to be the modern military. Guitar playing is probably all they do now, so they do that one thing well. To be fair, they play the same riff over and over.....
Nightmare Fuel: Comedy though it may be, the dystopia this movie portrays is disturbingly similar to how many people feel every day. Sometimes one can't help but wonder.
As noted above on xkcd, the "many people who feel that way" have been around for countless generations, each time assuming that they are superior to the next generation.
Unfortunate Implications: If this movie weren't a silly comedy and instead had a more serious tone, it would be easy to accuse it of endorsing eugenics.