Continuity mistake: Lenny tells the prison guards they can check his sound system, and the guard on the back grabs the shotgun with his left hand. Shot changes, and the shotgun is back in his right hand, and he is repeating all previous movements.
Continuity mistake: Luthor and Lenny drive past a red and white truck and a Maglite billboard. A shot later, they drive past them again.
Revealing mistake: When Clark receives Lex's signal, he rushes out of the room where Lois and Lacy are. First, he crouches behind a couch and disappears. Then the camera pans to the right, and now he's Superman. Problem is, one can still see Clark's stand-in crouching behind the couch, revealing how the trick was achieved.
Continuity mistake: At the hotel room, when Superman rushes and leaves, Lois runs towards the window. A shot later, she is gone, only to reappear an instant cut later.
Continuity mistake: When Superman and Lois end their flight, her legs are stretched down, about to land on the ground. An instant cut later, they're bent, and she is lowering her legs again.
Other mistake: Nuclear and Lacy are floating in space, not moving at all, but their hair moves strongly as if in an earthly breeze.
Revealing mistake: After Superman sets the Statue back in place, he lands on the ground and the wall behind wobbles, revealing where the movie was retouched to hide the wires.
Continuity mistake: When Nuclear Man steals the Statue of Liberty, its color keeps swapping between blue and green all the time.
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.
Revealing mistake: When Nuclear Man blows the first manhole cover up, you can see the small plug-like device that was in the barrel of the ejector device as it flips over.
Other mistake: As Superman flies past the subway train, it's obvious that the train is sitting still, as the view of the tunnel shown it is stationary.
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 walks to the UN there's a mounted police man on the right. Shot changes, and he's suddenly on the far left. Shot changes again, and he's now meters ahead, on the left of the UN entrance.
Visible crew/equipment: When Clark watches the subway train leave a stage light is reflected on the carriage.
Continuity mistake: Nuclear man flies over the Russian parade and looks to his right. Then stops and stares in front and shoots fire balls at the tank below. Problem is the parade, tank and everything is taking place behind him (a matte painting). Laserdisc and international extended editions).
Continuity mistake: When Nuclear Man approaches the tornado the clouds and tornado move at normal speed except for the shot of Nuclear in front of the tornado, where it moves in slow motion. Later on, before the family exits the house the tornado moves in slo-mo again. (Laserdisc and international extended editions).
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 Lois visits sick Clark his fringe changes style from brushed to messy to messier between shots, back and forth.
Continuity mistake: When Lois' car arrives at the UN the rear window swaps between rolled up or down between shots.
Continuity mistake: When Superman walks towards the UN entrance there's a lot of people between him and the red car. A shot later the people have vanished and him and the kid are standing right next to the car.
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.