Continuity mistake: During the volcano eruption the animal on the right (goat or sheep, I don't know) keeps changing from brown colour to white.
Continuity mistake: When Superman throws the rock into the volcano, it flies from right to left into a huge cloud of smoke. In the following angle, it is falling from the blue clear sky, up away from the smoke.
Continuity mistake: When the volcano erupts, a wide shot shows a group of people behind the cop and the priest. In the following shot a woman appears in front of the cop.
Continuity mistake: After the SWAT van is lifted, it tilts forward. A frame later, it's looking sideways.
Continuity mistake: The cab's hood, crumpled by Nuclear Man's power beam, magically smoothes itself a frame later.
Continuity mistake: The rock that hits the prop-astronaut blows his head off. Seconds later the head is back in place.
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.
Continuity mistake: When Clark is about to enter the subway train, the people by the door and on the platform appear and disappear all the time: A cop, a man with a hat, a lady in a leather jacket.
Continuity mistake: When Superman throws Nuclear Man down the chimney, the sky is grey and cloudy, but a second later it's pitch black.
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.
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.
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.
Continuity mistake: After the volcano erupts, the boy standing to the right of the girl disappears between shots.
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.
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.
Continuity mistake: In the museum, while the guide is walking towards Superman's hair, people suddenly appear on the left taking pictures.
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.
Continuity mistake: While Superman flies with Lois, the sky keeps changing colour all the time.
Continuity mistake: When the statue of Liberty is about to crash on the street, a close shot is seen of jammed cars and hysterical people. When the shot changes to Superman flying to the rescue, the jam, the cops and the people have disappeared, and all is nice and quiet in Metropolis.
Continuity mistake: When the volcano erupts, there's suddenly a lot more snow on the crater.
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.