Revealing mistake: The elevator cables that Superman holds should be greasy, or at least dirty, but they are not, revealing he's merely holding a black rope.
Continuity mistake: When Luthor and Superman exit to the balcony to meet Nuclear Man, Superman gives a step down. A frame later he is up, and several seconds later he steps down again.
Continuity mistake: During the Great Wall of China scene, a tree suddenly appears by the wall just when Superman is leaving.
Revealing mistake: After Nuclear Man rampages Metropolis, Superman cries "Stop!" and a SWAT agent descends from the sky on visible wires.
Continuity mistake: When the baddies are waiting for Lex Luthor to arrive, before he fires them, the position of the cork on the table changes between shots.
Continuity mistake: When Nuclear Man arrives at the Statue of Liberty he lowers his arms twice.
Continuity mistake: On the terrace, when Superman and nuclear Man are about to fight, the rope next to the lamp on the wall keeps changing positions between shots.
Revealing mistake: While Nuclear Man and Superman are falling off the balcony, their skin switches from pink to natural. When Nuclear Man finally flies away he loses all of his colour and becomes semi transparent.
Revealing mistake: While flying with Lois, Superman lets her go and when he picks her up all of the wires holding him are visible.
Continuity mistake: While Superman is picking up the crystal form the hole in the barn, the straw hanging loose around the hole disappears in the wide shot.
Continuity mistake: When Lois goes out to fly with Superman, her coat is thrown on the couch, when she arrives, it is neatly folded. Superman couldn't have done it because he was away with her all the time and when he arrives he goes straight to his bedroom.
Continuity mistake: Nuclear Man lands on Metropolis and all the traffic in both lanes is jammed and no cars move. When he walks a couple of feet suddenly the right lane, which had space for a car the most, is empty and with space enough to let two taxis appear from nowhere and run for several feet.
Continuity mistake: While the subway is running loose, Lois stares at something, an immediate POV reveals it's the bystanders on the platform. But this is all wrong, the train is inside a pitch black tunnel all the time.
Continuity mistake: A fireman tries to grab the hose from the back of the truck and wounds himself. But half a second before there was no fireman there.
Revealing mistake: When the volcano erupts, it's obviously a painting because the lava doesn't flow or move an inch.
Continuity mistake: Superman walks to a building in front surrounded by grass and with no people or traffic nearby. However, immediately after, a close-up shows him approaching a totally different place, crowded with people and a traffic jammed street.
Continuity mistake: When Superman flies together with Lois his hair moves a lot because of the wind; but when he flies alone it stays perfect.
Continuity mistake: Clark Kent exits the hotel, gets in a car, changes into Superman and flies straight up to Lois's bedroom, which is a few stories above. So why is he shown flying over rooftops?
Continuity mistake: When Perry White goes up the escalator, he places both hands on the rail. A second later there's just one.
Visible crew/equipment: When Lois is freefalling, Superman catches her and, for a brief glimpse, you see two stage lights reflected on his glasses.
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.