Continuity mistake: When Superman flies towards a mountain, the lava on the volcano behind him disappears.
Continuity mistake: In class, Jeremy has his body bent over his desk. When the angle changes he is sitting properly on the chair.
Continuity mistake: At the Great Wall of China, Nuclear Man points his hands forward and explodes the wall in front. As of then, there's no continuity between the position of his hands and the location of the places exploding.
Continuity mistake: When Lenny leads his car with the cops in, the car is facing a very short road ending in a small mount of rocks. The following wider angle shows a very wide open space with grass and a huge cliff.
Continuity mistake: When Superman enters the UN hall, a back shot shows the people in the upper bleacher clapping, but a frame later, the front shot shows them sitting still.
Continuity mistake: While the crowd follows Superman to the UN, the man with the balloons is first seen far away from him, but half a second later he is very close.
Continuity mistake: When Nuclear Man is destroying Metropolis his hair suddenly changes from messy to perfectly brushed.
Continuity mistake: Seen from inside the train-driver's seat, the tunnel is darker and with lights on both sides, but a shot of the tunnel alone shows it brighter and with no lights on the left side. Then it cuts back to the previous angle and everything changes back.
Continuity mistake: Nuclear Man lands in Metropolis and the cab driver on the left swaps several times from having his arm inside the car in the wide angles, to outside the cab's window in the close-ups.
Continuity mistake: When Mrs. Warfield waits for Clark in her office, there's a white sculpture on the table. From the back it's away from a brown object, from the front it's very close to it.
Continuity mistake: When Superman leads nuclear man inside the building to find lacy, an old man turns sideways to let Super in. A frame later he is back facing the door.
Continuity mistake: When Superman cools the huge river of lava, a bunch of fresh white and red carnations can be seen inches away. Perhaps they are an ultra-heat-proof breed?
Continuity mistake: A window shop with a red curtain and a TV set explodes and gets totally destroyed, but several seconds later when Nuclear Man plays around with the SWAT van we see it intact.
Continuity mistake: When Luthor and Superman exit to the balcony to meet Nuclear Man, Superman gives a step down. A frame later he is up, and several seconds later he steps down again.
Continuity mistake: During the Great Wall of China scene, a tree suddenly appears by the wall just when Superman is leaving.
Continuity mistake: When the baddies are waiting for Lex Luthor to arrive, before he fires them, the position of the cork on the table changes between shots.
Continuity mistake: When Nuclear Man arrives at the Statue of Liberty he lowers his arms twice.
Continuity mistake: On the terrace, when Superman and nuclear Man are about to fight, the rope next to the lamp on the wall keeps changing positions between shots.
Continuity mistake: While Superman is picking up the crystal form the hole in the barn, the straw hanging loose around the hole disappears in the wide shot.
Continuity mistake: When Lois goes out to fly with Superman, her coat is thrown on the couch, when she arrives, it is neatly folded. Superman couldn't have done it because he was away with her all the time and when he arrives he goes straight to his bedroom.
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.