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.
Revealing mistake: After Superman leaves the Statue of Liberty, a thick string is noticeable under his cape to keep it up and fluttering.
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.
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: 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.
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: 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.
Answer: It was made on a very low budget. Golen - Golbus productions bought the rights to Superman. They were mostly known for B-Movies with not so big name stars. It was there attempt to play with the big studios. Plus at least 45 minutes of scenes were cut out, with major subplots.
In addition to budget cuts, they kept shortening the runtime, meaning scenes needed to be cut. The comic book adaptation has the uncut scenes and makes much more sense.