Revealing mistake: Many shots of Nuclear Man flying are reused throughout the movie.
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.
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.
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.
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).
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.
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.
Revealing mistake: All of the shots of Nuclear Man flying, or him turning around to check for Superman are the same ones repeated over and over again.
Revealing mistake: During the tornado scene, the wind makes the windows open and close violently, but the cowboy hat on the porch stays in place barely moving. (Laserdisc and international extended editions).
Revealing mistake: When Lacy floats in space, Superman saves her and heads towards Earth. When he comes back, the shot of the Earth behind is the same one from before, yet reversed.
Revealing mistake: When the volcano erupts and lava floods the village. The red truck on the left is a very obvious scale model prop: The engine is missing and the hood is attached to the grilles.
Revealing mistake: When Nuclear Man melts the rifle, note that the SWAT member is holding the barrel and he slides his hand away slowly to make the barrel bend downwards. He was obviously holding it up. If he had burned himself he would've moved faster.
Revealing mistake: When the fire truck explodes, note a tube behind it going straight to the truck. Probably an FX device to effect the smoke.
Revealing mistake: When dying and balding Clark grabs the green glass, the border of his wig noticeably protrudes all around his face.
Revealing mistake: When Superman discovers that Nuclear Man is stealing the Statue of Liberty, he turns around and you can see the wrinkles on his temple from the wig he was using.
Revealing mistake: After the power plant 'swallows' Nuclear Man, the needle meters have the word AUTODIESEL UXBRIDGE written inside. Uxbridge is the British city where the scene was shot, therefore not the fictional Metropolis.
Revealing mistake: Obvious doll replaces Nuclear Man when he falls into the chimney.
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.