Deliberate mistake: There's no way Lois Lane, a beat reporter for the Daily Planet, could afford living in a penthouse apartment.
Suggested correction: There are plenty of ways for her to afford it. For instance, maybe it belongs to a wealthy relative who lets her stay there when they are out of town. Since any explanation would be irrelevant to the plot, there is no reason for the movie to waste time on it.
Plot hole: After Superman has reversed time the Hoover Dam reverts to its previous undamaged state as it should, but Jimmy Olsen should then have been replaced back on the dam. Instead he interrupts the potential kiss between Lois and Superman and complains of being abandoned by Superman in the desert.
Suggested correction: Superman is moving at speeds fast enough to turn back time. He can spend 5 seconds to yank Jimmy away from the top of a dam he knows is going to be destroyed just to be safe in case he can't actually stop it all from happening again.
Plot hole: Superman could have easily caught both missiles, proven by how fast we see him flying around the globe just a few minutes later. He's fast enough to circle the globe multiple times in seconds, but struggles for minutes to catch the missile.
Suggested correction: Superman had never flown that fast before in the movie. It could be argued that he was still in the process of discovering and pushing the limits of his powers and it was the emotional episode of losing Lois that motivated him to push himself.
Stupidity: Given his speed, surely Superman could've stopped both missiles with no problem.
Continuity mistake: When Superman catches the cat burglar, when viewed from inside the window the soles of his boots are red. After Superman saves Lois and flies away from the daily planet building his soles are black.
Suggested correction: After he flies away from Lois, the bottoms of his boots are visible for only a couple of frames. Mistakes that require freeze framing are not valid.
