Audio problem: When Nuclear Man puts Lenny down on the floor, Lenny babbles some things but his mouth doesn't move.
Continuity mistake: When Superman lands near the UN, Lois and Jimmy disappear from the crowd, only to appear half a second later, in the closer angle.
Continuity mistake: The Soviet missile has legible CCCP red letters, but in the following shot it's covered in snow, although the close-ups don't show any snow falling.
Continuity mistake: Outside the UN, the hot dog in the kid's hand suddenly disappears.
Continuity mistake: Superman is on the moon, about to cause the sun eclipse, and flies to the left, as if he were to exit the moon. In the next shot Superman is seen coming from the void towards the moon again.
Continuity mistake: When Lois is packing Superman's cape and Lacy says "I had nothing to do with it", there's no continuity with the passers-by seen behind. A kid in a red t-shirt, for example, appears from nowhere.
Continuity mistake: When Superman saves the girl from the Great Wall of China and starts rising, a woman with a white hat behind lifts her arm to say goodbye. In the following angle she is repeating the movement.
Continuity mistake: Before nuclear Man lands in the city, there's barely any smoke. A split second later, the close shot is completely filled with smoke. Then it disappears when we see the old lady with the yellow bag, and reappears when we go back to Nuclear Man.
Revealing mistake: In the aerial shot of Nuclear Man entering the crater of the volcano the smoke coming from it is still, thus revealing it's a painting.
Continuity mistake: While Superman is in awe reading the "Drop dead" headline, there's a group of journalists on the background and an empty chair on the right. When Clark stands up, a man appears seated on the chair.
Continuity mistake: After Nuclear Man lands on Metropolis a black man in a grey suit keeps moving from a white pole to a parking sign between each shot.
Continuity mistake: In order to stop the eruption, Superman flies towards a mountain. Watch the central part of it and you'll notice that the wide and close shots are of completely different mountains. The volcano also swaps from having smoke to exploding between frames.
Continuity mistake: Clark runs towards the subway train and stops. Then from a different angle he is several meters behind, running and stopping again.
Continuity mistake: The smoke coming out of the volcano changes direction in a split second after nuclear Man enters the crater.
Continuity mistake: In the quarry, Lenny parks his car to the very right of two wagons. Seconds later the car is in front of them.
Continuity mistake: When Superman is rebuilding the Great Wall all of the people near the hole vanish.
Continuity mistake: When nuclear Man makes the engine of the taxi explode, there's a guy with a red jacket behind it that appears and disappears between shots.
Continuity mistake: Swat agents hide behind the van and start to shoot. A second later they've all vanished.
Continuity mistake: Superman walks towards the UN and there are benches in front of him. In the next wide angle they've disappeared.
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.