For the novel by J.G. Ballard and the 1996 film adaptation:
Audience-Alienating Premise: It's a novel about repulsive people both using and being used by each other, and also about their intense sexual attraction to car crashes. So alienating it literally got Ballard called "beyond psychiatric help."
Awesome Music: The opening title theme by Howard Shore, scored for multiple icy electric guitars, perfectly captures the weird, cold and yet highly eroticised atmosphere of the movie.
So Okay, It's Average: General opinion of the film is that it's not bad, per say, but ultimately the controversy overhyped it significantly.
For the 2004 film:
Anvilicious: One of the main criticisms against the film is that it dispenses Haggis's opinion on race very overtly, with its Loads and Loads of Characters seemingly doing nothing but talk about race.
Award Snub: A snub in Crash's favor - a number of critics and moviegoers felt that Crash won Best Picture not so much due to its quality as a film, but due to its anti-racism stance was "safer" compared to that of its chief competitor Brokeback Mountain, and it frequently gets brought up among the Academy's biggest mistakes over the years.
Crosses the Line Twice: There's a few instances of this, but Flanagan's weary declaration of "Fuckin' black people, right?" to Graham Waters, a black detective, really stands out. The latter's subtly astonished reaction really sells it.
Harsher in Hindsight: The scene where Officer Ryan molests Christine is even more uncomfortable in light of the accusations of sexual misconduct leveled at director Paul Haggis.
Assuming you buy into the idea that the film won Best Picture over Brokeback Mountain because the voters wanted to go with the less controversial message movie, it became quite ironic when writer/director Paul Haggis left Scientology a few years later over their support of Proposition 8.
Hype Backlash: It got a lot of this after it won Best Picture, especially since the film had come out long before the main awards season and many people had forgotten about it until the Oscars.
Jerkass Woobie: Graham Waters. He's a rather callous person, especially toward those close to him, and ultimately condemns a fellow police officer for gunning down a deranged undercover cop in self-defense. However, by the end of the movie it's clear that he's a good cop who does care about people and this fact is used to blackmail him into claiming the innocent white cop's killing of the guilty black one was racially motivated in order to protect his brother Peter. Which is then rendered pointless when he finds Peter murdered. And worst of all, his drug-addicted mother blames him for Peter's death. To add insult to injury, his mom believes Peter bought her groceries before he died, not knowing that Graham was the one who did while she was strung out. His look of utter defeat in the end is tragic.