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.
Artistic License - Physics: You really can't get into orbit by simply pointing up and gunning the engines. Rule of Cool makes it work, but it also makes Elysium seem very much closer and easier to get to: an Island In Space.
Anvilicious: Impoverished, Spanish-speaking citizens of Earth trying to illegally immigrate to a space station owned by the English/French-speaking 1%? Bonus points for name-dropping the Department of Homeland Security. Yeah, this film is totallysubtle with its allegories regarding illegal immigration, universal healthcare, and the Occupy movements. Then again, this is a movie made by the same guy who made District 9, which had all of the subtlety of a freight train. That being said, Some Anvils Need to Be Dropped.
Complete Monster: The truly psychotic Agent Kruger is first introduced shooting down refugee ships full of men, women and children. We are informed after of Kruger's history of human rights violations, a reputation that he proceeds to live up. He kills Max's allies and then when he tracks Max to the home of Max's old friend Frey, he threatens and beats Frey in front of the girl, mocking the girl to close her eyes as he claims he hates to commit violence in front of kids, before attempting to molest Frey. After Frey scorns him, he declares he'll make sure her daughter is never healed. When he's chastised for his failures by his superior Delacourt, Kruger simply murders her and then declares he'll take over Elysium itself to give it the ruler it deserves.
Crazy/Creepy Awesome: Kruger. For instance, he prefers barbecuing chicken and ribs with his katana.
Draco in Leather Pants: It's rare for a nigh-inhumane bastard to receive this treatment. However, Sharlto Copley's superlative performance as the Ax-Crazy Kruger makes this villain the runaway favorite for most viewers.
Ensemble Darkhorse: Spider, whose fast talking antics and his determination as a badass make him very charismatic.
Esoteric Happy Ending: Yes, all the people on Earth are now considered to be "citizens" and now they have free healthcare. It still doesn't solve the original problem that led to this situation in the first place and in fact will only making it much worse (overpopulation) and there might not be enough medpods for everyone.
Tough Act to Follow: Given that Neill Blomkamp's debut film was District 9, this reaction was kind of inevitable, unfortunately. While many praise this film for its effects and Sharlto Copley's performance as Kruger, quite a few thought that the social commentary and the overall character development paled in comparison to Blomkamp's debut film.
What an Idiot: Max sassing the robot policemen. That's something you really shouldn't be doing to regular policemen either, especially if you have a prison record.
What the Hell Is That Accent?: Delacourt's strange accent. She's the only character with an accent that doesn't sound like an existing modern one. Given that she's French, it's probably supposed to be a faint French accent over Foster's native American English.