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)
Other mistake: The part of the great wall of China that Superman fixes where bricks grow has nothing to do with the broken part from before, nor with the wall we see once he fixes it.
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.
Continuity mistake: When Nuclear Man is created he extends his fingers. Shot changes to a wide angle and they are bent and he is extending them again.
Audio problem: After the satellite crashes against the cosmonaut, inside the spaceship a Russian cosmonaut starts to cry out things, but his mouth isn't moving.
Other mistake: Nuclear and Lacy are floating in space, not moving at all, but their hair moves strongly as if in an earthly breeze.
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.
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 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).
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.