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.
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.
Continuity mistake: After lifting the car, for unknown reasons Superman has a visible dark blue bracelet on his right arm. (01:24:55)
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.
Continuity mistake: When Superman lifts Lex's car, Lex swaps between having his mouth open in awe to having it shut, between shots.
Revealing mistake: When Superman drops Nuclear Man down the power plant chimney, the city behind swaps from a real image to a cheap blurry painting.
Revealing mistake: During the Metropolis destruction, when a cab crashes against the cab in front, the first car's trunk blows out and the FX system (an air-bag similar system) to make this happen flies all over the place.
Revealing mistake: When Nuclear Man's fingers hurt Superman's nape, part of the Statue of Liberty's tablet disappears.
Continuity mistake: When Lex shows up at the base, walking by a door, the 5 soldiers guarding it a frame before disappear.
Revealing mistake: After Superman leaves the Statue of Liberty, a thick string is noticeable under his cape to keep it up and fluttering.
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.
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.