Continuity mistake: Nuclear Man breaks through the Daily Planet ceilings but his hair doesn't ruffle, instead it looks much better than when he entered the building. Superman's hair does ruffle and get messy and dirty.
Continuity mistake: The Russian cosmonaut who says, "Sing at home, Sinatra.", is floating relaxed inside the spaceship, a frame later he is crouched fixing some bolts.
Continuity mistake: When Lenny and Lex do the genetic experiment, the stuff on the table comes much closer together between the first and second shot.
Continuity mistake: In the barn Carl looks ahead to see through the walls to check who's coming. His POV shows a cart wheel, but when the angle changes it's been replaced by 4 stables. The wheel is on the far right hand side.
Revealing mistake: When Nuclear Man destroys Metropolis, one of the walls between the window shop wiggles and the tiles flutter revealing it's a cardboard set. (01:10:55)
Continuity mistake: When the volcano erupts, the village's main tower keeps swapping form lit to unlit between shots.
Revealing mistake: While Superman and Nuclear Man fall off the building and fight on air, they pass by the same parts of the building over and over again.
Continuity mistake: When Superman is being buried in the moon, the flag pole behind disappears between shots.
Revealing mistake: When Superman and Lois jump off the window, Lois passes by the same window over and over again.
Factual error: At the beginning of the movie we're told that the Statue of Liberty is in Metropolis. However, the subway billboard states that it's in New York.
Continuity mistake: At the hotel room, Clark and Lois are watching the city skyline. From their POV the city is New York/Metropolis, but behind them is a glass door which reflects the real city, which is completely different.
Continuity mistake: When Superman flies to save the cosmonaut, the spaceship behind turns pink.
Continuity mistake: Before rampaging Metropolis, Nuclear Man elevates himself in Luthor's apartment and smoke comes out of his arms. For the rest of the movie this feature doesn't happen.
Continuity mistake: In the barn, the vest is folded in such a way that the sleeve-hole is hidden. However, in the close-up of Carl hiding the glass the hole is perfectly visible. Then it swaps to the previous angle.
Continuity mistake: Before Lacy enters the elevator at the hotel lobby an old man walks behind Clark, but suddenly disappears when the angle changes.
Continuity mistake: In the hotel room, the swimming pool's waters are flat, then when Superman arrives at the terrace behind they are very rippled, then a frame later it cuts to Lois greeting Super and they are totally flat again.
Continuity mistake: When the movie starts, the cosmonaut is standing up straight on the spaceship. A frame later he is laying horizontally plus he is suddenly attached to some sort of tube.
Revealing mistake: When Clark receives Lex's signal, he rushes out of the room where Lois and Lacy are. First, he crouches behind a couch and disappears. Then the camera pans to the right, and now he's Superman. Problem is, one can still see Clark's stand-in crouching behind the couch, revealing how the trick was achieved.
Continuity mistake: At the hotel room, when Superman rushes and leaves, Lois runs towards the window. A shot later, she is gone, only to reappear an instant cut later.
Continuity mistake: When Superman and Lois end their flight, her legs are stretched down, about to land on the ground. An instant cut later, they're bent, and she is lowering her legs again.
Answer: There appears to be multiple reasons. They had creative differences, ultimately resulting in a poorly received movie. Kidder said Reeves, who co-wrote the story, had an inflated ego and clashed with Furie.
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Moreover, Mark Pillow, who played Nuclear Man, claimed that working with Reeve was quite intense.