Visible crew/equipment: After Superman leaves Lenny in school, he takes off and the wooden barrier of the platform ascending him is noticeable on the lower left side of the screen.
Revealing mistake: When Superman takes Lex's car to prison, right when Lex and Lenny become black and white, Lex is a blatant stunt double.
Continuity mistake: Lex is a bald man, except for this movie where he has very obviously natural hair.
Continuity mistake: When Superman lifts Lex's car, Lex swaps between having his mouth open in awe to having it shut, between shots.
Revealing mistake: When Superman drops Nuclear Man down the power plant chimney, the city behind swaps from a real image to a cheap blurry painting.
Revealing mistake: During the Metropolis destruction, when a cab crashes against the cab in front, the first car's trunk blows out and the FX system (an air-bag similar system) to make this happen flies all over the place.
Revealing mistake: When Nuclear Man's fingers hurt Superman's nape, part of the Statue of Liberty's tablet disappears.
Continuity mistake: When Lex shows up at the base, walking by a door, the 5 soldiers guarding it a frame before disappear.
Revealing mistake: After Superman leaves the Statue of Liberty, a thick string is noticeable under his cape to keep it up and fluttering.
Continuity mistake: When Luthor is about to enter the military bunker, there's a truck right next to the entrance with a young soldier standing next to it. When the angle changes, the truck is far away and the soldier is a different guy.
Continuity mistake: When Lex walks by the military bunker the blinds are opened. When he is inside, they're closed.
Revealing mistake: When the missile is launched, Superman flies to catch it. However, his face has some sort of stocking over the upper part and the man looks nothing like Christopher Reeve. It was either a stunt double, a bad special effect, or a cheap mannequin.
Continuity mistake: When Superman walks to the UN light casts a 1 o'clock shadow on the pavement, yet it disappears a frame later from a different shot.
Revealing mistake: When Nuclear Man lands in Metropolis before destroying everything, watch the truck and cab on the left and you'll realise that they are a painting. Not a realistic painting, but a cheap, unfinished one.
Visible crew/equipment: When the cosmonaut is fixing some cables, a crew member's hands holding the camera are reflected on his visor.
Revealing mistake: After Nuclear Man bursts the cab's hood, watch behind and you'll see the wiggling cable that pulls the prop car.
Revealing mistake: The first time we see Clark, he is crossing the crowded street towards the subway entrance. Note that none of the cars are moving except for a cab in the front. If you watch behind Clark you'll see that the street ends in a flat wall, revealing it's a backlot set.
Revealing mistake: When the movie ends and Superman grabs Lenny and Lex's car, they both become black and white coloured and semi transparent.
Revealing mistake: Underneath Lenny's car when it flies away in the quarry there's no pipes, no nothing, just a black plank, revealing the car's a cheap prop.
Continuity mistake: When the firemen are grabbing the hose, the black car on the left turns around 180ยบ and changes model between shots. Also, the yellow cab on the right changes positions and model, notice its headlights changing styles between shots.
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.