Revealing mistake: When the subway train is supposedly running wild, watch the man to the left of Lois: He throws Lois's book violently away on the sly, as if the (fake) rumble inside the train had done the mess.
Continuity mistake: Nuclear Man sends the 2 police cars back and the one on the right skids and faces slightly to the right, but a second later, when they explode, both cars are perfectly aligned.
Continuity mistake: When Lacy shows the mock front page of the Daily Planet she holds it covering the red circle on the top right. A frame later she's holding it several inches down.
Continuity mistake: When Nuclear Man sends the police cars back, there's a man close to a mailbox on the left. There's a very brief cut before the cars explode but when the explosion takes place, the man has vanished.
Factual error: Superman and Nuclear Man fly around the world fighting at incredible speed. Everywhere they go, including places as widely spread as New York and China, it's daytime.
Visible crew/equipment: When Nuclear Man's laser beams send Superman flying away on the moon, the shadow of the crane moving him is visible.
Continuity mistake: Nuclear Man lands on a street surrounded by skyscrapers. In the following shots where he destroys everything, the right side of the street is the same, but the left side is totally different: small houses, sunnier, signs on the walls.
Continuity mistake: While the volcano explodes close to the Italian village, a man jumps off a balcony but disappears just a frame later from the following wide shot of the place.
Continuity mistake: A couple seconds after Lenny insults Nuclear Man, when he is about to be lifted up, the place he stands in is different from where he was before.
Audio problem: When Lex is giving instructions to launch the missile, a young man puts on his earphones and talks to Lex, but his mouth doesn't move.
Continuity mistake: In the hotel, right before Lacy enters the elevator, the hall of the hotel is filled with plants, couches and people. A second later, while Clark is on the trolley, the hall is a vast, empty place for the trolley to wander around.
Continuity mistake: When nuclear Man watches the newspaper on the table, the lighter is by the side of the phone. In the following shot it's in front of it.
Continuity mistake: When Lois gets in the train, the people next to her change completely between shots.
Continuity mistake: Before Superman rebuilds the Great Wall, he flies up with a woman in his arms. He flies past a stone arch and starts to descend. However, the following angle shows him yards behind descending right by the center of the arch.
Continuity mistake: Before Lex presses the red button to launch the missile, the phone next to it is hung-up. Then someone grabs it and the phone cable covers the control panel, but the immediate close-up of Lex's finger shows that the phone is hung-up, as in the first position.
Continuity mistake: The bundle that Superman makes to destroy the weapons changes to a tenth of its size in about a second.
Revealing mistake: Although Lois and another passenger move violently to show that the train is running wild, the rest of the passengers and the straps to hold one self remain perfectly still.
Other mistake: When the visitors are leaving the museum, the first man from the cue stares at the camera for a brief moment.
Visible crew/equipment: When Nuclear Man enters the building after being told he would be taken to Lacy, he flys upward through different floors. As he's doing this you can see support wires attached.
Continuity mistake: By the colour of the new stones repaired, you can tell that the first gap that Superman fixes at the Great Wall is smaller in size and triangular shaped, instead of the original rectangular and huge gap made by Nuclear Man.
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.