Continuity mistake: When the firemen are about to grab the hose and it explodes, note that the other hose inside the truck on the right side has changed positions between shots.
Continuity mistake: Nuclear Man walks towards the newspaper where Lucy's picture is, for a brief moment there's a light smoke coming from behind him as if something was burning (it has nothing to do with the smoke Nuclear produces when flying) which is later gone (according to SupermanIV.com a deleted scene involved Nuclear Man waking up, "he sees and picks up the newspaper with Lacy, which then catches on fire in his hand.").
Continuity mistake: Before Nuclear Man see Lacy's picture in the newspaper, he rises from the floor and a wide angle reveals that the table is nowhere around, yet a couple shots later it simply appears half a meter away from him.
Revealing mistake: When dying and balding Clark grabs the green glass, the border of his wig noticeably protrudes all around his face.
Continuity mistake: When Lois visits sick Clark she stands by the door, fully lit, a frame later, when the angle changes, the whole place is in the shadows.
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.
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.
Audio problem: When Lex enters the military bunker, officer Goram's voice is obviously dubbed and sometimes the audio doesn't match his lips.
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.
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.
Continuity mistake: When Superman throws Nuclear Man down the power plant, Nuclear's black wristbands disappear and reappear between shots.
Revealing mistake: Obvious doll replaces Nuclear Man when he falls into the chimney.
Visible crew/equipment: Obvious stunt double for Christopher Reeve when lifting the lady to the China Wall; note his thick sideburns, big forehead and skinny build.
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.
Revealing mistake: When Superman meets Nuclear Man at the terrace, the blue-screen surrounding the set is reflected on the windows.
Visible crew/equipment: After Superman leaves Lenny in school, he takes off and the wooden barrier of the platform ascending him is noticeable on the lower left side of the screen.
Revealing mistake: When Superman takes Lex's car to prison, right when Lex and Lenny become black and white, Lex is a blatant stunt double.
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.