Continuity mistake: When Clark is in Lacy's kitchen watching Lex's message, the billboard underneath changes between shots.
Continuity mistake: When Superman lands with Lois after flying around, he says "You don't know my name." Right then her bangs swaps from messy and uneven to evenly cut and brushed.
Continuity mistake: Superman's X-ray vision cooks the raw turkey and then the shot cuts to Superman's face, when it returns to the turkey is perfectly cook and now has a skinny leg on the right side.
Continuity mistake: When Superman lifts Lenny and Lex's car up in the air, Lenny's hand is inside the vehicle, but a frame later it's outside and further back.
Continuity mistake: Nuclear Man breaks through the Daily Planet ceilings but his hair doesn't ruffle, instead it looks much better than when he entered the building. Superman's hair does ruffle and get messy and dirty.
Continuity mistake: The Russian cosmonaut who says, "Sing at home, Sinatra.", is floating relaxed inside the spaceship, a frame later he is crouched fixing some bolts.
Continuity mistake: When Lenny and Lex do the genetic experiment, the stuff on the table comes much closer together between the first and second shot.
Continuity mistake: In the barn Carl looks ahead to see through the walls to check who's coming. His POV shows a cart wheel, but when the angle changes it's been replaced by 4 stables. The wheel is on the far right hand side.
Continuity mistake: When the volcano erupts, the village's main tower keeps swapping form lit to unlit between shots.
Continuity mistake: When Superman is being buried in the moon, the flag pole behind disappears between shots.
Continuity mistake: At the hotel room, Clark and Lois are watching the city skyline. From their POV the city is New York/Metropolis, but behind them is a glass door which reflects the real city, which is completely different.
Continuity mistake: When Superman flies to save the cosmonaut, the spaceship behind turns pink.
Continuity mistake: Before rampaging Metropolis, Nuclear Man elevates himself in Luthor's apartment and smoke comes out of his arms. For the rest of the movie this feature doesn't happen.
Continuity mistake: In the barn, the vest is folded in such a way that the sleeve-hole is hidden. However, in the close-up of Carl hiding the glass the hole is perfectly visible. Then it swaps to the previous angle.
Continuity mistake: Before Lacy enters the elevator at the hotel lobby an old man walks behind Clark, but suddenly disappears when the angle changes.
Continuity mistake: In the hotel room, the swimming pool's waters are flat, then when Superman arrives at the terrace behind they are very rippled, then a frame later it cuts to Lois greeting Super and they are totally flat again.
Continuity mistake: When the movie starts, the cosmonaut is standing up straight on the spaceship. A frame later he is laying horizontally plus he is suddenly attached to some sort of tube.
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: 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.
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.