Continuity mistake: While the subway is running loose, Lois stares at something, an immediate POV reveals it's the bystanders on the platform. But this is all wrong, the train is inside a pitch black tunnel all the time.
Continuity mistake: A fireman tries to grab the hose from the back of the truck and wounds himself. But half a second before there was no fireman there.
Continuity mistake: Superman walks to a building in front surrounded by grass and with no people or traffic nearby. However, immediately after, a close-up shows him approaching a totally different place, crowded with people and a traffic jammed street.
Continuity mistake: When Superman flies together with Lois his hair moves a lot because of the wind; but when he flies alone it stays perfect.
Continuity mistake: Clark Kent exits the hotel, gets in a car, changes into Superman and flies straight up to Lois's bedroom, which is a few stories above. So why is he shown flying over rooftops?
Continuity mistake: When Perry White goes up the escalator, he places both hands on the rail. A second later there's just one.
Continuity mistake: In the very beginning of the film, a satellite dish next to the Russian cosmonaut keeps appearing and disappearing.
Continuity mistake: When Lacy is seducing Clark in the office, she places her left leg on the table, several inches away form the edge. From the opposite angle it's on the very edge of the table.
Continuity mistake: When Lacy is seducing Clark, he is sitting straight, but in the following angle he is leaning backwards with his head tilted sideways.
Continuity mistake: When Superman catches -and saves- the cosmonaut, the russian's boots change from silver to dark grey.
Continuity mistake: When Superman is given a baseball bat, the angle changes and the position of the shadows reflected on the barn change completely.
Continuity mistake: When the Russian spaceship is spinning round, the bright and orange light inside and its minimal decoration are totally different to the inside shots, with a dim light and cables and stuff everywhere.
Continuity mistake: Before Superman throws the heavy weights at the gay gym instructor, two small weights are laying parallel on the floor. A second later one has moved underneath the bench.
Continuity mistake: When Superman flies towards the Russian cosmonaut his space suit changes from silver to green.
Continuity mistake: When Nuclear Man lets go the the Statue of Liberty, he disappears in the immediate wide angle shot.
Continuity mistake: When Superman is about to take the Russian cosmonaut back inside his spaceship, a first angle shows him very close to the doorway. A shot later he is farther away.
Continuity mistake: Before Luthor introduces Nuclear Man to Superman, they have a chat next to the bar. The bottles and figurine on the back changes positions between shots.
Continuity mistake: When Superman misses hitting the baseball, the ball's position on the floor changes between shots.
Continuity mistake: After Superman prevents the Statue of Liberty from crashing against the street, when he passes Central Park, there's a wide angle of the Statue flying and Superman is nowhere to be seen.
Continuity mistake: When Superman arrives at Lois's balcony, a plant on the left is away from the door. When Superman leaves and Lois asks him to take her with him, the plant is next to the door.
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.