Other mistake: Nuclear and Lacy are floating in space, not moving at all, but their hair moves strongly as if in an earthly breeze.
Factual error: While in space, Superman and Nuclear Man's capes are flapping. Since it is a vacuum, there is no air, therefore the capes shouldn't flap. Likewise, on the moon, the dust and dirt are moving too quickly to be in a micro gravity situation.
Continuity mistake: When Lois drives to the UN Lacy is not in the car. Half a second later she appears inside.
Continuity mistake: When Superman flies to save the girl inside the tornado and the family exits the basement there's a truck by the entrance door filled with hay. Half a second later the truck is gone and reappears behind the family, but now it's empty. (Laserdisc and international extended editions).
Continuity mistake: When the movie begins, the cosmonaut has some sort of big compass attached to his legs that disappears in the wide shots.
Revealing mistake: When Lacy floats in space, Superman saves her and heads towards Earth. When he comes back, the shot of the Earth behind is the same one from before, yet reversed.
Other mistake: When Lois and Superman fly together, the part where they fly over some horses is the very same shot as when they fly over the Golden Gate for the second time.
Other mistake: When Superman breaks his ice cage and makes it explode, a long black rubber band flies away. Where the heck did that come from?
Revealing mistake: When Nuclear Man melts the rifle, note that the SWAT member is holding the barrel and he slides his hand away slowly to make the barrel bend downwards. He was obviously holding it up. If he had burned himself he would've moved faster.
Factual error: Superman places the nuclear missiles in the giant disposable bag in space, throws them at the sun, and the bag burns up when it hits the sun. In reality, the bag would have burned up long before hitting the sun. (00:35:35)
Revealing mistake: Obvious doll replaces Nuclear Man when he falls into the chimney.
Continuity mistake: Lex is a bald man, except for this movie where he has very obviously natural hair.
Visible crew/equipment: When Superman saves the cosmonaut, stage lights are reflected on his visor.
Revealing mistake: When Nuclear Man flies through the ceiling for the first time, the first glass he crashes into is noticeably different than the others surrounding it, revealing it's a prop.
Other mistake: When Lenny has the prison guards locked in the car and is putting the top up, the steering wheel is spinning but the front wheels aren't moving. The amount of revolutions of the steering wheel is mechanically impossible also.
Continuity mistake: After Superman ducks the moon rock, there's a close-up of Nuclear Man's black boot stepping on Superman's boot, yet in the next angle, it's Nuclear Man who's yelling in pain. It should be Superman instead.
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.