Visible crew/equipment: While Nuclear Man destroys Metropolis, a bunch of people appear behind him, specially a woman with a white gabardine, a funny wig, dark glasses and a big fake nose. She reappears in a totally different place two seconds later, when the police cars arrive.
Continuity mistake: In the very beginning of the film, a satellite dish next to the Russian cosmonaut keeps appearing and disappearing.
Continuity mistake: When Lacy is seducing Clark in the office, she places her left leg on the table, several inches away form the edge. From the opposite angle it's on the very edge of the table.
Continuity mistake: When Lacy is seducing Clark, he is sitting straight, but in the following angle he is leaning backwards with his head tilted sideways.
Continuity mistake: When Superman catches -and saves- the cosmonaut, the russian's boots change from silver to dark grey.
Continuity mistake: When Superman is given a baseball bat, the angle changes and the position of the shadows reflected on the barn change completely.
Continuity mistake: When the Russian spaceship is spinning round, the bright and orange light inside and its minimal decoration are totally different to the inside shots, with a dim light and cables and stuff everywhere.
Continuity mistake: Before Superman throws the heavy weights at the gay gym instructor, two small weights are laying parallel on the floor. A second later one has moved underneath the bench.
Continuity mistake: When Superman flies towards the Russian cosmonaut his space suit changes from silver to green.
Continuity mistake: When Nuclear Man lets go the the Statue of Liberty, he disappears in the immediate wide angle shot.
Continuity mistake: When Superman is about to take the Russian cosmonaut back inside his spaceship, a first angle shows him very close to the doorway. A shot later he is farther away.
Continuity mistake: Before Luthor introduces Nuclear Man to Superman, they have a chat next to the bar. The bottles and figurine on the back changes positions between shots.
Continuity mistake: When Superman misses hitting the baseball, the ball's position on the floor changes between shots.
Revealing mistake: When Superman returns the cosmonaut back in the spaceship, Superman's head becomes transparent, and the cosmonaut's helmet becomes wobbly, all because of the use of blue-screen.
Continuity mistake: After Superman prevents the Statue of Liberty from crashing against the street, when he passes Central Park, there's a wide angle of the Statue flying and Superman is nowhere to be seen.
Continuity mistake: When Superman arrives at Lois's balcony, a plant on the left is away from the door. When Superman leaves and Lois asks him to take her with him, the plant is next to the door.
Continuity mistake: When Lacy is seducing Clark in the office, the things on the table change positions between shots. Watch how the glasses move around, for example.
Continuity mistake: Nuclear Man is destroying Metropolis and always, behind him, there is a white truck and a lot of cars. But in one of the shots the cars have vanished and a lot of people appear.
Continuity mistake: After Superman straightens the Russian spaceship, he flies away to save the cosmonaut. In the following wide angle he is flying towards a different direction.
Plot hole: After Nuclear Man slides down the chimney of the Nuclear Plant the lid of the reactor is open and then automatically closes. This whole premise is totally absurd, not only for security reasons, but for logical ones too.
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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