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.
Continuity mistake: When Superman and Lois are flying together, the train below drives from right to left, but half a second later it is moving in the opposite direction.
Continuity mistake: After Lois and Clark read the headline with the "Drop dead" to kid, shots alternate between each of them and there's no sync in the graphics appearing on the computers behind each, while for the rest of the whole film all computers are in sync.
Continuity mistake: After the volcano erupts, a big black cloud covers the city, but a wider angle shows the sky clear.
Continuity mistake: After nuclear Man crumples the cab's hood, there's another taxi behind starting to drive slowly towards the damaged cab. A frame later, a new angle shows that taxi repeating the previous movements but really fast.
Audio problem: When Nuclear Man knocks out Superman on the moon we hear some growling, but their mouths aren't moving.
Continuity mistake: The SWAT van is lifted next to the curb, but a second later appears in the middle of the street surrounded by cars.
Continuity mistake: Luthor extends his arm with a dollar bill in hand for Nuclear Man to light. From the front his arm is fully extended. From behind it isn't.
Continuity mistake: When the SWAT van is turning around, the cars on the street are different than the ones in previous shots (try to find the destroyed taxi cabs that collided).
Continuity mistake: When Nuclear Man is thrown down the chimney, he is unconscious with his arms and head looking down. A frame later he is stiff, with his arms up and pointing to the sky.
Revealing mistake: While flying together, Superman let's go of Lois and she plummets at first, but then, with the snowy mountains behind, she's able to float on air and keep on moving at the same time for 5 seconds.
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.