Revealing mistake: After Nuclear Man destroys the cab's hood, the shot changes and there's a thick string running behind him all along the car, and the cab driver is stretching out to pull it. Probably he was activating some sort of bad FX.
Revealing mistake: When Nuclear Man hits Superman by the Statue of Liberty's grounds, Superman reacts to the kick before actually being hit.
Revealing mistake: When Superman saves the people that Nuclear Man throws up into the air, as they lower you can see the support wires holding them up.
Revealing mistake: When the net full of nuclear missiles is thrown into the sun, the footage of the explosion is exactly the same as the explosion of the single rocket with the DNA of Nuclear Man attached.
Revealing mistake: Watch the moon fight between the two supermen. In one scene, Superman charges nuclearman and you can see the backdrops flutter if your monitor brightness is high.
Revealing mistake: When NuclearMan goes to destroy the Great Wall of China, there is a brief glimpse of him wearing support wires.
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.
Revealing mistake: Before Superman brings the cosmonaut safely to his spaceship the entrance door wiggles as if made of cardboard. There's no air in space and it's supposed to be a strong, solid structure.
Revealing mistake: In this scene, all the SWAT cops have the same type of rifle, except for the guy that gets his melted by Nuclear Man, which is a thick rubbery prop.
Revealing mistake: Near the end of the movie, Superman descends on the tower, by the elevator room, and his supporting wires are visible.
Revealing mistake: When Superman flies towards the volcano, the scene of the eruption he is superimposed on is exactly the same one we saw 2 minutes earlier.
Revealing mistake: When Superman drops the elevator containing the imprisoned Nuclear Man on the moon, he flies off and lands to straighten the American flag. In this shot you can plainly see the wires helping him land.
Revealing mistake: After they fall off the balcony, Superman chases Nuclear Man, but the boats beneath don't move.
Revealing mistake: After Nuclear-Man kicks Superman in the air after putting the Statue of Liberty back, Superman does flips and part of him disappears.
Revealing mistake: When the subway train is supposedly running wild, watch the man to the left of Lois: He throws Lois's book violently away on the sly, as if the (fake) rumble inside the train had done the mess.
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.
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.
Revealing mistake: While the subway train is gone wild, there's a brief shot of bystanders on the platform. Then the train keeps going on for several seconds, and when it finally comes to a stop the actors are the same ones used previously.
Revealing mistake: When Lenny's car, with the cops in it, flies into the air you can see it's empty.
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.