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.
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.
Revealing mistake: Same footage used when the Statue of Liberty plummets and when it's lifted up by Superman, though reversed.
Revealing mistake: Superman's hands move despite him being frozen in a block of ice.
Revealing mistake: Reversed scene when Nuclear Man exits the volcano: note the white smoke climbing upwards into the crater.
Revealing mistake: When the first cab is attacked by Nuclear Man, watch underneath and you'll notice that the wheels don't touch the ground, revealing it's a prop.
Revealing mistake: When Nuclear Man steals the Statue of Liberty, there's a very obvious blur around the retouched image where the real statue has been painted over to simulate it's gone.
Revealing mistake: When the police cars drive backwards, before they crash and burst, the scene is a repetition of a previous one but reversed.
Revealing mistake: During the subway sequence, all of the train stations are always the same Metropolis South.
Revealing mistake: When Nuclear Man destroys Metropolis, one of the walls between the window shop wiggles and the tiles flutter revealing it's a cardboard set. (01:10:55)
Revealing mistake: While Superman and Nuclear Man fall off the building and fight on air, they pass by the same parts of the building over and over again.
Revealing mistake: When Superman and Lois jump off the window, Lois passes by the same window over and over again.
Revealing mistake: When Lacy floats in space, Superman saves her and heads towards Earth. When he comes back, the shot of the Earth behind is the same one from before, yet reversed.
Revealing mistake: When Nuclear Man melts the rifle, note that the SWAT member is holding the barrel and he slides his hand away slowly to make the barrel bend downwards. He was obviously holding it up. If he had burned himself he would've moved faster.
Revealing mistake: Obvious doll replaces Nuclear Man when he falls into the chimney.
Revealing mistake: When Nuclear Man flies through the ceiling for the first time, the first glass he crashes into is noticeably different than the others surrounding it, revealing it's a prop.
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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