Continuity: At the beginning of the film, Clark wakes up in his bed. There is a close-up of his eyes. They are brown. However, during the rest of the film, Clark's eyes are blue.
Hadn't thought about that one... that's pretty lazy.
Continuity: When the series of tremors causes the globe on top of The Daily Planet Headquarters to topple and fall, Superman catches it and places it on a car. When he flies away that night, at the end of the movie, and the camera spans Metropolis behind him, it sits in its original position on top of the Headquarters.
Hmm... I was under the impression that he was in the hospital for days? Maybe I just assumed that...