Continuity mistake: When Superman first meets Mr Warfield, the orange pencil on the table changes positions between shots.
Continuity mistake: When Superman stops the train there are two thick black tubes next to the tunnel behind which disappear when he leaves.
Continuity mistake: The white box that Lex attaches to the missile, containing Nuclear Man's 'ingredients', appears and disappears between shots.
Continuity mistake: When Nuclear Man is born, both hands are clenched. He opens and extends the right one first, then the left. A frame later the right hand is slightly clenched again.
Continuity mistake: The Daily Planet Building lobby is a completely different one between the scenes where Nuclear Man destroys Metropolis and the one where Warfield is fired.
Continuity mistake: When Superman throws Nuclear Man down the power plant, Nuclear's black wristbands disappear and reappear between shots.
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: After lifting the car, for unknown reasons Superman has a visible dark blue bracelet on his right arm. (01:24:55)
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: The driver of the SWAT van disappears when the van is standing upright. (01:14:00)
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.
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.