Continuity mistake: Amount of rock from the cut-out mountain standing out from crater differs between the first and second shot.
Revealing mistake: When the first cab is attacked by Nuclear Man, watch underneath and you'll notice that the wheels don't touch the ground, revealing it's a prop.
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.
Revealing mistake: When Nuclear Man steals the Statue of Liberty, there's a very obvious blur around the retouched image where the real statue has been painted over to simulate it's gone.
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.
Revealing mistake: When the police cars drive backwards, before they crash and burst, the scene is a repetition of a previous one but reversed.
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.
Visible crew/equipment: During the city attack, after Nuclear attacks a bus, a boom mic is reflected on a cab's windshield. (01:10:25)
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.
Continuity mistake: After Nuclear brakes the cab's hood, the opening width of the trunk changes between one frame and another in between angles for no reason whatsoever.
Continuity mistake: When Clark is in Lacy's kitchen watching Lex's message, the billboard underneath changes between shots.
Continuity mistake: When Superman lands with Lois after flying around, he says "You don't know my name." Right then her bangs swaps from messy and uneven to evenly cut and brushed.
Continuity mistake: Superman's X-ray vision cooks the raw turkey and then the shot cuts to Superman's face, when it returns to the turkey is perfectly cook and now has a skinny leg on the right side.
Continuity mistake: When Superman lifts Lenny and Lex's car up in the air, Lenny's hand is inside the vehicle, but a frame later it's outside and further back.
Revealing mistake: During the subway sequence, all of the train stations are always the same Metropolis South.
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.