Other mistake: When Clark Kent enters the subway, the set is the same as the rampage later in the film; only that the second time we see this set, the subway entrance has vanished.
Continuity mistake: When the satellite knocks the Russian cosmonaut, they are both dragged into space, but the immediate wide angle shows him alone in the void, no sign of the huge satellite.
Continuity mistake: While Superman walks to UN, the way Jimmy holds his camera changes in a split second.
Continuity mistake: When nuclear Man bursts the cab's hood, the radiator explodes and vanishes. A second later it's back on.
Continuity mistake: When Lois gets in the subway train it is packed with people, in the close shot they are gone.
Continuity mistake: When Superman and Nuclear Man fight on the balcony the high powered binoculars disappear.
Continuity mistake: After smashing his head, Superman sends Nuclear Man flying away. At first, Nuclear Man is conscious and with his head pointing upwards. A frame later he is unconscious and the head is laying down.
Continuity mistake: Before Clark steps down off the trolley, a group of people surrounded by suitcases are seen on the back, but disappear when the angle changes.
Continuity mistake: When Nuclear Man is destroying Metropolis, the same stuntman with a gabardine and a hat is seen close to a shop window, then a second later in the middle of the street and a second afterwards getting thrown through the air with a group of people. He looks and dress just like Clark Kent, guess it's his stand in doing some extra work.
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.
Continuity mistake: The Statue of Liberty manages to fall down straight the whole long time, but when it is is about to hit the ground, the angle changes and the statue has magically tilted sideways.
Other mistake: Nuclear Man is shown blowing up the Great wall twice, but it's the same shot reversed.
Continuity mistake: When Superman falls straight and unconscious off the Statue of Liberty he's facing a 9 o'clock direction. In the next angle he is facing 5, then lands facing 7.
Continuity mistake: When the lava is flooding the village, a big green plant appears close to a priest. When Superman cools the lava and the smoke goes away, we see that the plant is much smaller and less leafy.
Continuity mistake: When Superman takes off after saving the boy in the Great Wall of China scene, you see him heading up, as if leaving, but in the next cut, he's on the ground next to the wall.
Continuity mistake: Lex's fat assistant enters the place with the missiles' control panels. Outside he is seen entering through an open door. From the inside, the door is closed and he enters a second later.
Continuity mistake: When Nuclear Man lands on Metropolis a cop on the right is opening the door of his car. In the next shot he is repeating the movement.
Continuity mistake: When Nuclear Man arrives to earth, full of energy from the sun, his footsteps don't glow; neither do they when he arrives to the balcony, several scenes later. Then a couple of seconds after they glow but stop glowing when he walks towards Superman and keep that way for the rest of the film.
Continuity mistake: When Superman is taking the missile with the rest of the weapons, its colour changes from dark black to light grey.
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.