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 His POV shows a cart wheel, but when the angle changes it's been replaced by 4 stables.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.
Continuity mistake: When the volcano erupts, the village's main tower keeps swapping form lit to unlit between shots.
Continuity mistake: When Superman is being buried in the moon, the flag pole behind disappears between shots.
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.
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.