Continuity mistake: When the volcano erupts, there's suddenly a lot more snow on the crater.
Continuity mistake: When the statue of Liberty is about to crash on the street, a close shot is seen of jammed cars and hysterical people. When the shot changes to Superman flying to the rescue, the jam, the cops and the people have disappeared, and all is nice and quiet in Metropolis.
Continuity mistake: Nuclear Man lands on a street surrounded by skyscrapers. In the following shots where he destroys everything, the right side of the street is the same, but the left side is totally different: small houses, sunnier, signs on the walls.
Continuity mistake: Before Lex presses the red button to launch the missile, the phone next to it is hung-up. Then someone grabs it and the phone cable covers the control panel, but the immediate close-up of Lex's finger shows that the phone is hung-up, as in the first position.
Continuity mistake: The bundle that Superman makes to destroy the weapons changes to a tenth of its size in about a second.
Visible crew/equipment: When Nuclear Man enters the building after being told he would be taken to Lacy, he flys upward through different floors. As he's doing this you can see support wires attached.
Continuity mistake: In a split second, all of the snow on the mountain cut by Superman disappears.
Continuity mistake: On the moon, nuclear Man grabs a rock with a huge hole underneath and holds it over his head. The angle changes and the rock has changed to a different one with a solid bottom.
Revealing mistake: During the tornado, when the little girl cries by the window check the lower corner of the window on the right and you'll see the white string moving the window. (Laserdisc and international extended editions).
Revealing mistake: Right after Lex, disguised as a soldier, orders the launching of the missile, there's a shot of the truck carrying it. The driver is a cheap mannequin that looks very much like a scarecrow.
Revealing mistake: Due to the blue-screen effect, part of Superman's glasses disappear when he is free falling with Lois.
Continuity mistake: Seen from inside the train-driver's seat, the tunnel is darker and with lights on both sides, but a shot of the tunnel alone shows it brighter and with no lights on the left side. Then it cuts back to the previous angle and everything changes back.
Revealing mistake: When in space, Superman punches Nuclear Man on the back, he turns around and his face has turned blurry and black, but his body keeps the same colour. In the immediate close-up the face's colour is fixed.
Visible crew/equipment: Nuclear Man descends close to the statue of liberty to fight Superman. For a brief glimpse his supporting wires are seen.
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.
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: 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).
Revealing mistake: Many shots of Nuclear Man flying are reused throughout the movie.
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.
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.