Continuity mistake: After Nuclear Man lands on Metropolis a black man in a grey suit keeps moving from a white pole to a parking sign between each shot.
Continuity mistake: In order to stop the eruption, Superman flies towards a mountain. Watch the central part of it and you'll notice that the wide and close shots are of completely different mountains. The volcano also swaps from having smoke to exploding between frames.
Continuity mistake: Clark runs towards the subway train and stops. Then from a different angle he is several meters behind, running and stopping again.
Continuity mistake: The smoke coming out of the volcano changes direction in a split second after nuclear Man enters the crater.
Continuity mistake: In the quarry, Lenny parks his car to the very right of two wagons. Seconds later the car is in front of them.
Continuity mistake: When Superman is rebuilding the Great Wall all of the people near the hole vanish.
Continuity mistake: When nuclear Man makes the engine of the taxi explode, there's a guy with a red jacket behind it that appears and disappears between shots.
Continuity mistake: Swat agents hide behind the van and start to shoot. A second later they've all vanished.
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.
Revealing mistake: When Lois and Superman are flying together, they turn green, specially Lois's arms and hands.
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.
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.