Other mistake: Something that happens a lot in films. When Lex Luthor is watching the cops trail Otis the image on Lex's CCTV screen is actually just the scene from the film being played back. The shots change to angles where Lex couldn't possibly have a camera, for instance a close up on the cop holding his partner's hat. This mistake is especially more noticeable in the extended edition where Superman walks through Lex's 'gauntlet'.
Continuity mistake: Near the end of the movie when Superman pulls Lois Lane out of the car and she's already dead, she is very dirty all over because of all the dirt that "drowned" her. In the following shot when Superman is done crying over her and leaves her on the ground to reverse time so that she will come to life again, her clothes are all white and shiny.