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.
Continuity mistake: After Clark reads the 'Drop Dead' cover, he stands up and walks down the newsroom, all puzzled. The number of people and their positions has no continuity at all between shots.
Continuity mistake: The same man next to Lois on the train is standing on the platform a second later.
Continuity mistake: After the "Drop dead" cover, Jimmy Olsen talks to Lois. In the close-up of Lois while she says "He looks like my father," the journalist behind her is standing up. An instant cut later, he is seated.
Continuity mistake: When Nuclear Man steals the Statue of Liberty, its pedestal looks normal. When Superman puts it back in place, the pedestal is missing a huge chunk (surely because of some FX going wrong). In further shots, it's fixed.
Revealing mistake: When Superman and Nuclear Man fall down the building, their capes remain stuck to their backs, defying the laws of gravity, and thus revealing that the scene was shot with them standing up and then turning the camera around.
Continuity mistake: When Moscow's Red Square scene begins, the tanks and soldiers parade in front of the authorities (a combination of matte painting and a real set). When Superman arrives, a second tree has appeared next to the one on the left. On the right side, an unfinished painting has replaced the previous huge wall, trees, and decor. (International theatrical, TV, and LaserDisc releases).
Visible crew/equipment: When Superman saves the day in Moscow, the edge of the set and the backlot behind can be seen on the sides of the wall where the politicians stand. One can even see the set's scaffolding on the right. (International theatrical, TV and LaserDisc releases.)
Continuity mistake: Before Nuclear Man finds the newspaper with Lacy's photo, he is at Lex's lair kneeling down, then starts to fly. Big clouds of smoke come out of his wrists, but an instant cut later in the close-up, the smoke is gone.
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.
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.