Continuity mistake: Before Luthor introduces Nuclear Man to Superman, they have a chat next to the bar. The bottles and figurine on the back changes positions between shots.
Continuity mistake: When Superman misses hitting the baseball, the ball's position on the floor changes between shots.
Continuity mistake: After Superman prevents the Statue of Liberty from crashing against the street, when he passes Central Park, there's a wide angle of the Statue flying and Superman is nowhere to be seen.
Continuity mistake: When Superman arrives at Lois's balcony, a plant on the left is away from the door. When Superman leaves and Lois asks him to take her with him, the plant is next to the door.
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.
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.
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).
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.
Continuity mistake: Lenny tells the prison guards they can check his sound system, and the guard on the back grabs the shotgun with his left hand. Shot changes, and the shotgun is back in his right hand, and he is repeating all previous movements.
Continuity mistake: Luthor and Lenny drive past a red and white truck and a Maglite billboard. A shot later, they drive past them again.
Continuity mistake: At the hotel room, when Superman rushes and leaves, Lois runs towards the window. A shot later, she is gone, only to reappear an instant cut later.
Continuity mistake: When Superman and Lois end their flight, her legs are stretched down, about to land on the ground. An instant cut later, they're bent, and she is lowering her legs again.
Continuity mistake: When Nuclear Man steals the Statue of Liberty, its color keeps swapping between blue and green all the time.
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.