Continuity mistake: When Superman catches the falling girl by the Big Wall, his hair is pointed upwards, obviously due to a big amount of hair fix to simulate a moving hair. A frame, later, from another angle, the hairstyle is different, no sign of the hair fix.
Continuity mistake: Lex is a bald man, except for this movie where he has very obviously natural hair.
Continuity mistake: When Superman lifts Lex's car, Lex swaps between having his mouth open in awe to having it shut, between shots.
Continuity mistake: When Lex shows up at the base, walking by a door, the 5 soldiers guarding it a frame before disappear.
Continuity mistake: When Luthor is about to enter the military bunker, there's a truck right next to the entrance with a young soldier standing next to it. When the angle changes, the truck is far away and the soldier is a different guy.
Continuity mistake: When Lex walks by the military bunker the blinds are opened. When he is inside, they're closed.
Continuity mistake: When Superman walks to the UN light casts a 1 o'clock shadow on the pavement, yet it disappears a frame later from a different shot.
Continuity mistake: When the firemen are grabbing the hose, the black car on the left turns around 180ยบ and changes model between shots. Also, the yellow cab on the right changes positions and model, notice its headlights changing styles between shots.
Continuity mistake: When Nuclear Man sees the newspaper, it smooths itself between shots.
Continuity mistake: When Clark hears Lois' cries for help he is by the edge of the subway platform. A frame later he is a meter away.
Continuity mistake: Position of thumb changes when Superman carries the Statue, before he is attacked by Nuclear Man.
Continuity mistake: Pavement swaps from dry to wet when the SWAT van is attacked.
Continuity mistake: Before the cop cars drive backwards and crash, all the cops around the cars disappear.
Continuity mistake: Nuclear Man's hair becomes shorter when he approaches to read the newspaper.
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.
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.