Continuity mistake: While Superman is taking the Statue of liberty back to its place the sky keeps changing between violet and blue, sunny and cloudy.
Continuity mistake: When Superman leaves Luthor in the quarry, he lands several feet to the right of the cop. In the close-up they are almost close to each other.
Continuity mistake: Shortage of extras in this film: Inside the UN hall, the arab man that greets Superman is the one that a second before was in the entrance, together with the woman with a pink handkerchief over her head.
Continuity mistake: When Superman lands Lex on the quarry, the standing position of the prisoner behind differs between shots.
Continuity mistake: After the two police cars are sent backwards, a third one that was parked behind, suddenly appears aligned with the other two.
Continuity mistake: When Lois is in the subway carriage crying for help, she places her right hand on the rail above. A frame later the hand is by her waist.
Continuity mistake: Before lava covers the Italian village, furniture under the two arches on the right, as well as a vase, cart wheel and table on the left disappear between shots.
Revealing mistake: When NuclearMan goes to destroy the Great Wall of China, there is a brief glimpse of him wearing support wires.
Continuity mistake: Nuclear Man arrives at Luthor's apt. and steps into a dark corner, where he loses his powers. From the opposite angle the place is filled with light, so Nuclear Man shouldn't have lost his strength.
Other mistake: The same front shot of Superman flying is used over and over and over again.
Continuity mistake: While Superman walks with the kid to the UN, the sky changes from sunny to cloudy in a nano-second.
Continuity mistake: In the gym, the amount of sport bags on the back differs between shots.
Revealing mistake: When Superman and Nuclearman are fighting for the first time in outer space, you can see them both standing on a small platform.
Revealing mistake: When Nuclear Man blows up the fire hydrant one can easily notice it's made of foam.
Visible crew/equipment: When Nuclear Man turns Luthor's assistant around on the air, supporting wires are visible.
Continuity mistake: While the lava flows on the Italian village, a wooden cart with hay on the left suddenly becomes a red car.
Continuity mistake: The debris on the bottom of the Statue of Liberty's base appears and disappears between shots.
Continuity mistake: Superman land on the middle-top of the missile, but a second later he is further down and on the side of it.
Visible crew/equipment: In the quarry, when the cops' car flies up the air you can see the ramp used to lift it on the lower left side of the screen.
Continuity mistake: When Nuclear Man fires at the fire truck a short piece of hose comes out. A second later, in the following shot, the hose is 10 meters long and all over the place.
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.