Continuity mistake: Nuclear Man lands in Metropolis and the cab driver on the left swaps several times from having his arm inside the car in the wide angles, to outside the cab's window in the close-ups.
Continuity mistake: When Mrs. Warfield waits for Clark in her office, there's a white sculpture on the table. From the back it's away from a brown object, from the front it's very close to it.
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.
Continuity mistake: When Superman leads nuclear man inside the building to find lacy, an old man turns sideways to let Super in. A frame later he is back facing the door.
Continuity mistake: When Superman cools the huge river of lava, a bunch of fresh white and red carnations can be seen inches away. Perhaps they are an ultra-heat-proof breed?
Continuity mistake: A window shop with a red curtain and a TV set explodes and gets totally destroyed, but several seconds later when Nuclear Man plays around with the SWAT van we see it intact.
Revealing mistake: The elevator cables that Superman holds should be greasy, or at least dirty, but they are not, revealing he's merely holding a black rope.
Continuity mistake: When Luthor and Superman exit to the balcony to meet Nuclear Man, Superman gives a step down. A frame later he is up, and several seconds later he steps down again.
Continuity mistake: During the Great Wall of China scene, a tree suddenly appears by the wall just when Superman is leaving.
Revealing mistake: After Nuclear Man rampages Metropolis, Superman cries "Stop!" and a SWAT agent descends from the sky on visible wires.
Continuity mistake: When the baddies are waiting for Lex Luthor to arrive, before he fires them, the position of the cork on the table changes between shots.
Continuity mistake: When Nuclear Man arrives at the Statue of Liberty he lowers his arms twice.
Continuity mistake: On the terrace, when Superman and nuclear Man are about to fight, the rope next to the lamp on the wall keeps changing positions between shots.
Revealing mistake: While Nuclear Man and Superman are falling off the balcony, their skin switches from pink to natural. When Nuclear Man finally flies away he loses all of his colour and becomes semi transparent.
Revealing mistake: While flying with Lois, Superman lets her go and when he picks her up all of the wires holding him are visible.
Continuity mistake: While Superman is picking up the crystal form the hole in the barn, the straw hanging loose around the hole disappears in the wide shot.
Continuity mistake: When Lois goes out to fly with Superman, her coat is thrown on the couch, when she arrives, it is neatly folded. Superman couldn't have done it because he was away with her all the time and when he arrives he goes straight to his bedroom.
Continuity mistake: Nuclear Man lands on Metropolis and all the traffic in both lanes is jammed and no cars move. When he walks a couple of feet suddenly the right lane, which had space for a car the most, is empty and with space enough to let two taxis appear from nowhere and run for several feet.
Continuity mistake: While the subway is running loose, Lois stares at something, an immediate POV reveals it's the bystanders on the platform. But this is all wrong, the train is inside a pitch black tunnel all the time.
Continuity mistake: A fireman tries to grab the hose from the back of the truck and wounds himself. But half a second before there was no fireman there.
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.