Continuity mistake: Superman walks towards the UN and there are benches in front of him. In the next wide angle they've disappeared.
Continuity mistake: When the train driver passes out, several (speeded-up) shots of the tunnel and the shots of the bystanders on the platform show that the train is moving really fast, but in between there's a shot of Lois at normal speed, and the lights of the tunnel seen through the windows show that the train speed is quite low.
Continuity mistake: When Nuclear Man destroys Metropolis, he stands by the Metropolis Tower entrance, but disappears and reappears randomly depending on the angle.
Continuity mistake: During the subway sequence, the carriage in front of Lois's is empty, but when the train comes to a stop it's packed with people.
Continuity mistake: When Clark is about to leave the hotel, a man appears by the dark car on the right in less than half a second.
Continuity mistake: When the bellboy picks up Clark with the baggage trolley, he makes a close turn to the right and drives parallel to the elevator. When the angle changes he is in a totally different position.
Continuity mistake: One of the general shots in the subway shows Superman flying slower than usual and inches away from the bystanders. The problem is that their coats and hair don't flutter nor do they notice him passing by or seem nervous in any way. However, the next close shot of their faces show them nervous and in awe at the action.
Continuity mistake: On the moon, nuclear Man grabs a rock with a huge hole underneath and holds it over his head. The angle changes and the rock has changed to a different one with a solid bottom.
Continuity mistake: After Perry White delivers his final speech a woman in a yellow dress goes up the escalator. In the following shot, no one's there.
Continuity mistake: While Nuclear Man is destroying Metropolis, two police cars get moved backwards. The first shot of the cars moving show a lot of people by a shop window. The angle changes to a close shot, with no people there, then back to the previous wide angle, now with the cars moving backwards, and the bunch of people reappear.
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.
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).
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.
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.
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.