Continuity mistake: When Nuclear Man arrives at the place for the first time Lenny is facing Luthor. A shot later he is facing backwards.
Continuity mistake: When Nuclear Man is created he extends his fingers. Shot changes to a wide angle and they are bent and he is extending them again.
Continuity mistake: When the satellite knocks down the cosmonaut, his helmet differs between the wide shots and the close-ups from smooth and with no details, to a real one, revealing the first one is a dummy.
Continuity mistake: The inside of the Russian spaceship differs between the outside shots as seen through the window, and the ones inside.
Continuity mistake: After Superman is pinned to the ground on the moon, he gets some dust on his suit and his hair is messed up, but in the following shots the dust is gone and his hair is perfectly combed back again.
Continuity mistake: From the aerial angle of the Russian parade, the trucks have already passed the tribune where the politicians are, but in the close-up they're many meters behind. (Laserdisc and international extended editions).
Continuity mistake: Superman flies towards the tornado, where the girl is, and "destroys" the tornado (or whatever it is he does), yet, for unknown reasons, Superman is suddenly seen miles away somewhere else, flying towards the tornado again and, what's even weirder: the girl is now floating on air. (Laserdisc and international extended editions).
Continuity mistake: When Superman leaves the farm, after the tornado, the basement doors swap from closed to opened between shots. (Laserdisc and international extended editions).
Continuity mistake: No soldiers are visible in the aerial angle of the Russian parade, but dozens in the immediate close-up. (Laserdisc and international extended editions).
Continuity mistake: When Superman blocks the Russian missile during the parade, its position keeps changing in every single shot. Sometimes it's close to the politicians, others away... This changes back and forth. (Laserdisc and international extended editions).
Continuity mistake: When Nuclear Man bombs the Russian truck during the parade, the politicians are standing apart, calmly. A frame later they are squeezed together horrified. This keeps changing half a dozen times. (Laserdisc and international extended editions).
Continuity mistake: When Jenny is about to be sucked by the tornado, the windows are banging violently. The shot changes to a wide angle of her flying away and the windows are opened wide and still, despite the tornado blowing. (Laserdisc and international extended editions).
Continuity mistake: The floating pliers behind the cosmonaut keep appearing and disappearing between shots.
Continuity mistake: The cosmonaut is fixing a satellite dish with his left arm but a frame later he's working with his right arm instead.
Continuity mistake: On the moon, Nuclear Man grabs a rock and dirt covers him totally, especially his armpit becomes black. A frame later, he's spotless.
Continuity mistake: When the volcano's lava floods the village, there's a wide shot of the mountains and the volcano and you can see that the lava is still running down the volcano, not near the village.
Continuity mistake: When the firemen are about to grab the hose and it explodes, note that the other hose inside the truck on the right side has changed positions between shots.
Continuity mistake: Nuclear Man walks towards the newspaper where Lucy's picture is, for a brief moment there's a light smoke coming from behind him as if something was burning (it has nothing to do with the smoke Nuclear produces when flying) which is later gone (according to SupermanIV.com a deleted scene involved Nuclear Man waking up, "he sees and picks up the newspaper with Lacy, which then catches on fire in his hand.").
Continuity mistake: Before Nuclear Man see Lacy's picture in the newspaper, he rises from the floor and a wide angle reveals that the table is nowhere around, yet a couple shots later it simply appears half a meter away from him.
Continuity mistake: When Lois visits sick Clark she stands by the door, fully lit, a frame later, when the angle changes, the whole place is in the shadows.
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.