Other mistake: When Superman and Lois are flying through the clouds, there are a number of shots in which we see Superman from Lois' point of view. If you look closely, you can see that Christopher Reeve is not being suspended in these shots, but is, in fact, kneeling to look as though he is flying. You can tell by the profile of the red trunks.
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'.