Continuity mistake: When the Olympic marathon runner holds the torch while running on the track toward the stairs, he has a large upper body build. Also, his shirt has a very noticeable logo that is lying right on his sternum. As he climbs the stairs we see him from behind and this is the last of the real footage from the Olympics. The actor holding the torch, that gets blown out, does not climb the stairs near as gracefully as the Olympic athlete. When they show him from the front, not only does he have very little upper body muscle, but his face is nowhere near the same as the athlete in the stock footage. (01:12:10)
Other mistake: Towards the end of the movie, when Superman drops Gus off at the coal mine, Gus begins talking with the coal miners about him and Superman. He then rips open his shirt (as if he had a Superman costume on underneath). How did Gus know that Clark Kent tore his shirt like that in order to change into Superman, or keeps his suit under his clothes at all? The only people who know this fact are the ones who have seen the transformation from Clark to Superman, i.e. the audience.
Continuity mistake: When Gus is falling from the building on his skis the sky changes colour from shot to shot.
Continuity mistake: When Superman enters the acid storage room we have a glance at the temperature needle and can see it is way to the right; but the chemist is calm and no alerts are active. Minutes later, before the place explodes, while Superman is freezing the lake, the lights in the room turn red and the chemist freaks out, but the needle is further from the danger zone than it was when we first saw it.