Deliberate mistake: In the shot near the end of the film where Donnie grabs the keys for the station wagon, you can see a Blockbuster Video member card in a cup. That card design wasn't used until the mid to late 1990's. This movie is set in 1988. Deliberate as it's a product placement, but still wrong.
Deliberate mistake: During the "Sparke Motion" dance scene, the dance instructor is mouthing the wrong words to the song the girls are dancing to. "West End Girls" by the Pet Shop Boys was originally going to be the dance number, and that is actually the song playing for the recording of the scene. Richard Kelly couldn't get permission to use it, and "Notorious" by Duran Duran was substituted. The teacher is plainly mouthing words from the wrong song.