Factual error: If the Russian cosmonauts need special suits to survive out in space, so should Lacy when she is abducted by Nuclear Man. (00:02:50 - 01:20:20)
Continuity mistake: Nuclear Man dents the floor with his footsteps, but in a wider angle the floor is intact.
Continuity mistake: Two firemen are seen away from their truck, but when the angle changes six firemen have appeared seemingly from nowhere.
Continuity mistake: When Superman is walking with the kid towards the UN, they pass by a fire hydrant and one can see the street ahead is empty. A shot later another hydrant suddenly appears but the white benches disappear.
Suggested correction: The fire hydrant in question is actually two. The one they first pass is slightly faded with chipped paint. The next shot you see a different one that is fully painted red. The next shot shows the crowd passing the first hydrant seen.
Continuity mistake: When in the subway, Superman is standing by a 6 foot poster of the Statue of Liberty. When the shot changes to a flying Superman, he is a third of his size and the poster is huge.
Continuity mistake: Clark enters the barn to fiddle with his green crystal. When he exits, a huge amount of stuff from his childhood has magically appeared around the place.
Continuity mistake: Before lava covers the Italian village, furniture under the two arches on the right, as well as a vase, cart wheel and table on the left disappear between shots.
Other mistake: The same front shot of Superman flying is used over and over and over again.
Continuity mistake: While the lava flows on the Italian village, a wooden cart with hay on the left suddenly becomes a red car.
Visible crew/equipment: In the quarry, when the cops' car flies up the air you can see the ramp used to lift it on the lower left side of the screen.
Other mistake: When Clark Kent enters the subway, the set is the same as the rampage later in the film; only that the second time we see this set, the subway entrance has vanished.
Continuity mistake: When Superman and Nuclear Man fight on the balcony the high powered binoculars disappear.
Revealing mistake: In this scene, all the SWAT cops have the same type of rifle, except for the guy that gets his melted by Nuclear Man, which is a thick rubbery prop.
Other mistake: Nuclear Man is shown blowing up the Great wall twice, but it's the same shot reversed.
Continuity mistake: During the volcano eruption the animal on the right (goat or sheep, I don't know) keeps changing from brown colour to white.
Continuity mistake: The cab's hood, crumpled by Nuclear Man's power beam, magically smoothes itself a frame later.
Factual error: When Superman addresses the UN, the delegate presumably representing the United Kingdom appears behind an "England" sign - "England" is not an international entity represented at the UN, while the United Kingdom of Great Britain and Northern Ireland is. (00:32:20)
Continuity mistake: The rock that hits the prop-astronaut blows his head off. Seconds later the head is back in place.
Continuity mistake: When Lacy is about to enter the elevator, a light brown rug has appeared on the floor behind, which disappears in the next wide shots.
Continuity mistake: When the volcano erupts, there's suddenly a lot more snow on the crater.