Continuity mistake: During the Metropolis attack, the sky alternates from cloudy to sunny.
Continuity mistake: Nuclear walks towards the newspaper with Lacy's picture and moves his right arm to grab it. A frame later his arm is still, resting by his side.
Continuity mistake: Before Nuclear Man sees Lacy's picture he flies up and produces a big cloud of smoke, which disappears a frame later from a different angle.
Continuity mistake: Lacy flirts with Clark and places her left hand all along his shoulder. A frame later her hand is close to his neck.
Continuity mistake: At the hotel Jeremy walks to meet Mr. Warfield. In the first angle of him entering there's a bellboy walking in front, yet a frame later, from a close-up, the bellboy is now standing still a couple of meters behind.
Continuity mistake: Nuclear Man kicks Superman and sends him flying hundreds of meters away from the Statue of Liberty towards the sea, but Superman's cape falls down straight from above the torch.
Continuity mistake: When Superman activates his laser vision to cut a mountain he moves his head from right to left, but from his POV the laser beam hasn't appeared yet, plus when it does its position doesn't match Superman's head.
Continuity mistake: Lois opens Clarks's door and stands in the shadows talking to him. The amount of light by the door swaps from gloomy to totally lit depending on the angle, with no order whatsoever.
Continuity mistake: Superman holds the tip of the mountain with his body straight, as if standing on air, yet a frame later his body is laying along as when he flies.
Continuity mistake: When Nuclear Man first shows up, a sculpture to his left appears and disappears between shots.
Continuity mistake: Amount of rock from the cut-out mountain standing out from crater differs between the first and second shot.
Continuity mistake: Lex greets Nuclear Man extending his hand parallel to the floor. A frame later the hand is tilted sideways, perpendicular to the floor.
Continuity mistake: A US flag appears and disappears from Lacy's table when she flirts with Clark.
Continuity mistake: When Superman is locked inside a block of ice, the first shots shows it's semi-transparent, but a frame later it's opaque.
Continuity mistake: Nuclear Man crashes through Lacy's ceiling to abduct her, producing a perfect squared hole, with lamps on each side. When he exits, the hole is smaller and with an irregular shape, plus the lamps are further apart than before.
Continuity mistake: When the Statue of Liberty plummets, the building behind changes style, and also swaps from bronze to concrete.
Continuity mistake: When Luthor steals the strand of hair, Lenny stands inches away from him. A frame later he is in a different position 3 meters away.
Continuity mistake: When Clark sees Lex's building, there's no terrace anywhere, but when he arrives, a huge, wide terrace with an umbrella and plants around suddenly appears.
Continuity mistake: Lois visits sick Clark and opens the door wide. When the angle changes the opening is much narrower.
Continuity mistake: When Lacy acts sexy in her office, Clark is about to enter through her door, but when the angle changes he's 15 meters behind walking towards the door again.
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.