Continuity mistake: Nuclear Man is destroying Metropolis and always, behind him, there is a white truck and a lot of cars. But in one of the shots the cars have vanished and a lot of people appear.
Continuity mistake: After Superman straightens the Russian spaceship, he flies away to save the cosmonaut. In the following wide angle he is flying towards a different direction.
Continuity mistake: Clark holds the 'Drop dead' paper with his right hand. An instant later, he holds it with both hands.
Continuity mistake: When Superman leaves Lenny at the school, a group of kids gather around the gate. On the far right there's one with a red hat, an Afro-American boy with a football, and one with a jacket who grabs the gate. A shot later these last two have vanished but can be seen in the background, metres behind. When the priest exits, half a second later, half a dozen more boys have appeared seemingly out of nowhere.
Continuity mistake: When Perry White dismisses Warfield, a woman in yellow walks towards the escalators. A shot later, the escalators are empty, and she is walking towards them again.
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.
Continuity mistake: When Nuclear Man steals the Statue of Liberty, its color keeps swapping between blue and green all the time.
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.
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 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.
Continuity mistake: After flying together, Clark and Lois walk into the apartment. When she says she has "the jeepers" her arm suddenly swaps from lowered to raised.
Continuity mistake: In space Superman saves Lacy and flies away with her next to his right side. A shot later she is now on the left.
Continuity mistake: During the Moon fight, Superman is kicked in the head. He puts his right hand on his head, but a shot later his arm is lowered.
Continuity mistake: Clark grabs the crystal with both hands, and slowly starts retrieving his left hand. When the shot changes, his left arm is in a totally different position. (01:12:15)
Continuity mistake: After flying with Lois, Superman walks away and is about to crash against the camera. He quickly dodges it by turning sideways. From the opposite angle he is walking straight.
Continuity mistake: When Nuclear Man arrives at the place for the first time Lenny is facing Luthor. A shot later he is facing backwards.
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.