Continuity mistake: There is a scene at the school, where Quentin and Nancy are talking by the lockers. Quentin is wearing a Joy Division shirt. The jacket he is wearing over the shirt keeps changing depending on whether it's a closeup of Quentin or a shot of both him and Nancy. You can easily tell, as the band's name is partially obscured during closeup and fully revealed when it's further away. This changes back and forth several times during that scene. Quentin doesn't move enough to warrant the jacket changing so noticeably.
Continuity mistake: When Nancy is in the drugstore and she keeps slipping in and out of sleep, Freddy is walking toward the camera running a finger blade on a pipe, and you can see there is a raised pipe joint just before the camera cuts to a rear view of Freddy, and the pipe joint that his finger blade was going to scrape has now gone.