Revealing mistake: After (superimposed) Superman stops the tornado, he flies away to the left. Instead, the farmer stares and moves his head to the right. The director forgot to tell him where the image would be placed. (Laserdisc and international extended editions).
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.
Audio problem: When Lois and Clark jump off the terrace, she cries his name. In the wide angle she moves her mouth but no sound is heard.
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.
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.
Continuity mistake: When the satellite knocks down the cosmonaut, his helmet differs between the wide shots and the close-ups from smooth and with no details, to a real one, revealing the first one is a dummy.
Continuity mistake: The inside of the Russian spaceship differs between the outside shots as seen through the window, and the ones inside.
Continuity mistake: When the movie begins, the cosmonaut has some sort of big compass attached to his legs that disappears in the wide shots.
Revealing mistake: When Nuclear Man destroys Metropolis he sends beams to make things explode, but there's a moment when there are no beams seen and shops explode for no reason at all.
Continuity mistake: After Superman is pinned to the ground on the moon, he gets some dust on his suit and his hair is messed up, but in the following shots the dust is gone and his hair is perfectly combed back again.
Revealing mistake: During the Metropolis destruction scene, Nuclear Man sends a SWAT truck spinning around. When he lifts it up with his rays coming from his hands, you can see the truck is being lifted up by a visible white wire.
Revealing mistake: After Superman escapes the block of ice he was imprisoned in, watch the next shot (as he flies back towards Earth) closely... in this shot, it's clear that the effect was achieved by using a rather cheap-looking Superman "doll" composited into the shot, and not Christopher Reeve. It practically looks like a Superman "action-figure" you could buy at the store.
Revealing mistake: When Lex cuts the strand of hair, the bottom of the cabinet breaks before the ball drops.
Revealing mistake: When Clark and Lois are talking in Lacey's apartment, there appear to be bubbles and waves in the pool. However, they do not move.
Continuity mistake: From the aerial angle of the Russian parade, the trucks have already passed the tribune where the politicians are, but in the close-up they're many meters behind. (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.