Continuity mistake: When Lacy is seducing Clark in the office, the things on the table change positions between shots. Watch how the glasses move around, for example.
Continuity mistake: Nuclear Man is destroying Metropolis and always, behind him, there is a white truck and a lot of cars. But in one of the shots the cars have vanished and a lot of people appear.
Continuity mistake: After Superman straightens the Russian spaceship, he flies away to save the cosmonaut. In the following wide angle he is flying towards a different direction.
Plot hole: After Nuclear Man slides down the chimney of the Nuclear Plant the lid of the reactor is open and then automatically closes. This whole premise is totally absurd, not only for security reasons, but for logical ones too.
Visible crew/equipment: Lighting screens are reflected on a hotdog seller's glasses when Superman walks to the UN.
Revealing mistake: When Nuclear Man carries the Statue of Liberty, its fingers turn semi-transparent, revealing the buildings behind.
Visible crew/equipment: A moving boom mic is reflected in a car's windshield when Nuclear Man causes the explosions in Metropolis.
Continuity mistake: When Nuclear Man arrives in Metropolis, the cab driver beside the police car is a middle-aged man with grey hair. In the very next shot, he suddenly becomes a young man with dark hair and a toupee.
Continuity mistake: Clark holds the 'Drop dead' paper with his right hand. An instant later, he holds it with both hands.
Continuity mistake: After Clark reads the 'Drop Dead' cover, he stands up and walks down the newsroom, all puzzled. The number of people and their positions has no continuity at all between shots.
Continuity mistake: The same man next to Lois on the train is standing on the platform a second later.
Continuity mistake: After the "Drop dead" cover, Jimmy Olsen talks to Lois. In the close-up of Lois while she says "He looks like my father," the journalist behind her is standing up. An instant cut later, he is seated.
Continuity mistake: When Nuclear Man steals the Statue of Liberty, its pedestal looks normal. When Superman puts it back in place, the pedestal is missing a huge chunk (surely because of some FX going wrong). In further shots, it's fixed.
Continuity mistake: When Superman leaves Lenny at the school, a group of kids gather around the gate. On the far right there's one with a red hat, an Afro-American boy with a football, and one with a jacket who grabs the gate. A shot later these last two have vanished but can be seen in the background, metres behind. When the priest exits, half a second later, half a dozen more boys have appeared seemingly out of nowhere.
Continuity mistake: When Perry White dismisses Warfield, a woman in yellow walks towards the escalators. A shot later, the escalators are empty, and she is walking towards them again.
Revealing mistake: When Superman and Nuclear Man fall down the building, their capes remain stuck to their backs, defying the laws of gravity, and thus revealing that the scene was shot with them standing up and then turning the camera around.
Continuity mistake: When Moscow's Red Square scene begins, the tanks and soldiers parade in front of the authorities (a combination of matte painting and a real set). When Superman arrives, a second tree has appeared next to the one on the left. On the right side, an unfinished painting has replaced the previous huge wall, trees, and decor. (International theatrical, TV, and LaserDisc releases).
Visible crew/equipment: When Superman saves the day in Moscow, the edge of the set and the backlot behind can be seen on the sides of the wall where the politicians stand. One can even see the set's scaffolding on the right. (International theatrical, TV and LaserDisc releases.)
Continuity mistake: Before Nuclear Man finds the newspaper with Lacy's photo, he is at Lex's lair kneeling down, then starts to fly. Big clouds of smoke come out of his wrists, but an instant cut later in the close-up, the smoke is gone.
Revealing mistake: Many shots of Nuclear Man flying are reused throughout the movie.
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.