Continuity mistake: When the volcano erupts, there's suddenly a lot more snow on the crater.
Continuity mistake: When the statue of Liberty is about to crash on the street, a close shot is seen of jammed cars and hysterical people. When the shot changes to Superman flying to the rescue, the jam, the cops and the people have disappeared, and all is nice and quiet in Metropolis.
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: 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.
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: In a split second, all of the snow on the mountain cut by Superman disappears.
Continuity mistake: On the moon, nuclear Man grabs a rock with a huge hole underneath and holds it over his head. The angle changes and the rock has changed to a different one with a solid bottom.
Revealing mistake: During the tornado, when the little girl cries by the window check the lower corner of the window on the right and you'll see the white string moving the window. (Laserdisc and international extended editions).
Revealing mistake: Right after Lex, disguised as a soldier, orders the launching of the missile, there's a shot of the truck carrying it. The driver is a cheap mannequin that looks very much like a scarecrow.
Revealing mistake: Due to the blue-screen effect, part of Superman's glasses disappear when he is free falling with Lois.
Continuity mistake: Seen from inside the train-driver's seat, the tunnel is darker and with lights on both sides, but a shot of the tunnel alone shows it brighter and with no lights on the left side. Then it cuts back to the previous angle and everything changes back.
Revealing mistake: When in space, Superman punches Nuclear Man on the back, he turns around and his face has turned blurry and black, but his body keeps the same colour. In the immediate close-up the face's colour is fixed.
Visible crew/equipment: Nuclear Man descends close to the statue of liberty to fight Superman. For a brief glimpse his supporting wires are seen.
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.
Revealing mistake: After Nuclear Man bursts the cab's hood, watch behind and you'll see the wiggling cable that pulls the prop car.
Revealing mistake: When Nuclear Man lands in Metropolis before destroying everything, watch the truck and cab on the left and you'll realise that they are a painting. Not a realistic painting, but a cheap, unfinished one.
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.