Continuity mistake: The rock that hits the prop-astronaut blows his head off. Seconds later the head is back in place.
Sacha
Factual error: When Superman addresses the UN, the delegate presumably representing the United Kingdom appears behind an "England" sign - "England" is not an international entity represented at the UN, while the United Kingdom of Great Britain and Northern Ireland is. (00:32:20)
Audio problem: On the moon, Superman smashes Nuclear Man's head against his knee. The clonk is heard before the hit (even forgetting that sound can't be heard on the moon).
Sacha Continuity mistake: Lois visits Clark and takes her coat off, folds it and places it on her arm. A frame later the coat is lying on the couch.
Sacha Continuity mistake: When Clark is about to enter the subway train, the people by the door appear and disappear all the time: A cop, a man with a hat, a lady in a leather jacket.
Sacha Revealing mistake: When Superman flies towards the volcano, the scene of the eruption he is superimposed on is exactly the same one we saw 2 minutes earlier.
Sacha Continuity mistake: When Superman throws Nuclear Man down the chimney, the sky is grey and cloudy, but a second later it's pitch black.
Sacha Continuity mistake: Lois visits Clark at his appartment and a wooden duck, with the head painted green and white and a black coloured body, appears on the table next to her.
Sacha Continuity mistake: Outside the UN, the crowd looks up to the sky and watch Superman come flying. When he lands, 2 seconds later, all the stunts on the first row are either gone or standing somewhere else. A kid on the right with dyed hair, for example, is now standing way behind the crowd.
Sacha Continuity mistake: On the Great Wall, a woman with a turquoise jacket stumbles and is about to fall off the edge. From a new angle two seconds later, she is three meters behind and stumbling towards the edge again.
Sacha Continuity mistake: After the volcano erupts, the boy standing to the right of the girl disappears between shots.
Sacha Other mistake: In the rest of Superman movies, whenever he used his eyes to do some trick a beam came out. In this (really cheap) movie the beam is gone.
Sacha Revealing mistake: When Superman drops the elevator containing the imprisoned Nuclear Man on the moon, he flies off and lands to straighten the American flag. In this shot you can plainly see the wires helping him land.
Continuity mistake: During the Great Wall of China scene, the sky changes from cloudy and grey in the shots involving people, to bright and sunny when the wall explodes.
Sacha 
Continuity mistake: When Lacy is about to enter the elevator, a light brown rug has appeared on the floor behind, which disappears in the next wide shots.
Sacha Continuity mistake: In the museum, while the guide is walking towards Superman's hair, people suddenly appear on the left taking pictures.
Sacha Continuity mistake: When Superman arrives at the UN, Jimmy Olsen stops in the middle of the street to take a picture of him. A shot later he's six feet behind a dark car.
Sacha Revealing mistake: After they fall off the balcony, Superman chases Nuclear Man, but the boats beneath don't move.
Sacha Audio problem: When Lenny drives his car into the quarry, the sound of his radio changes depending on where the car is; but when he drives away, suddenly it stays constant. It should have decreased, and increased when we get to the close-up.
Sacha Continuity mistake: While Superman flies with Lois, the sky keeps changing colour all the time.
Sacha 
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.