Revealing mistake: Outside the UN, a woman in a red coat appears behind the hot dog stand and when the angle changes to the opposite side, in front of her, she's also there.
Continuity mistake: When the Soviets are about to launch the missile in the snowy field, there are two soldiers on the right and a third with a black hat running away. A second later there are three soldiers plus the one with the black hat who's now there.
Continuity mistake: Before the firemen arrive at the truck, there's a lot of smoke around, but half a second later it's all gone.
Continuity mistake: Before Lacy opens the red car's door at the UN, a lot of people walk towards her and stand inches away. A second later they've vanished.
Continuity mistake: While Nuclear Man moves the 2 police cars backwards, the first shot shows the car on the right ahead of the other. A frame later, in a new angle, it is way behind the other car.
Continuity mistake: After Lenny calls Nuclear Man "experiment freako", the stool from the drum disappears.
Plot hole: When Nuclear Man isn't receiving daylight he "dies", yet when he dives into the volcano he manages to come out as if nothing happened.
Continuity mistake: When Lois is walking towards the subway carriage there's a cop controlling the passers by. When Clark walks by two seconds later the cop is gone. The train starts to move and we get a panoramic view of the station and, yes, the cop has definitely vanished.
Continuity mistake: The tornado rips off the farm's roof, but it magically reappears with the house in perfect state after Superman arrives with the girl. He didn't have time to fix it. (Laserdisc and international extended editions).
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).
Continuity mistake: When Luthor explains his plan to the three baddies the champagne bottle swaps between pointing at him or away. The glass next to the ice cube also moves nearer/further in different shots.
Continuity mistake: When Superman is walking with the kid towards the UN, the sun changes between shots.
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.
Continuity mistake: When Superman starts his speech at the UN, in the wide angle his arms are extended, but a frame later they're next to his body.
Continuity mistake: When the satellite hits the spaceship, the shots from inside show the spaceship turning around clockwise, yet in the outside shots it is moving randomly: up and down, clockwise and anti clockwise.
Other mistake: The subway carriage stops by the Statue of Liberty ad, however, the one reflected on the cabin's glass is a VW ad.
Revealing mistake: Due to the blue-screen effect, part of Superman's glasses disappear when he is free falling with Lois.
Visible crew/equipment: Boom mic reflected on the hood of the cop car's, during the city attack.
Plot hole: Nuclear Man sends laser beams pointing his arms and destroys everything around, yet when inside the Daily Planet, he sends beams to the elevator but absolutely nothing happens.
Visible crew/equipment: When Lenny lets the guards in you can see filming equipment reflected in the rear-view mirror of Lenny's car.
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.