Continuity mistake: When Nuclear Man is thrown down the chimney, he is unconscious with his arms and head looking down. A frame later he is stiff, with his arms up and pointing to the sky.
Continuity mistake: When the crowd follows Superman to the UN the mounted cop changes from being on the left side to the right.
Continuity mistake: When Nuclear Man walks towards the newspaper on the desk, the phone cable's position changes through shots.
Continuity mistake: Superman crosses flying the Golden Gate Bridge together with Lois, heading close to the bay area. Half a second later they are next to the bridge again.
Continuity mistake: When Superman stops the subway train, there's a black man with a moustache, red shirt and a gabardine suit in the first line. Then he manages to appear meters behind, despite the jam on the platform. Then Lois appears behind him. Then she magically disappears and he appears back on the front.
Continuity mistake: Lois hands the newspaper to Clark, with the headline "Superman says drop dead to kid", and a guy in a red shirt in the background stands up and leaves, followed by a bunch of people behind; in the following angle he is sitting down and the whole choreography is repeated.
Continuity mistake: After Clark takes the green crystal from the hole on the ground and hides it, the cloth covering the hole has a different position to how it looked a second before.
Continuity mistake: When Superman is out on the balcony with Lois, a tall, wide building is reflected on the glass behind, but when the angle changes to Superman's POV the building is gone, and now there's just a vast open space and a thin skyscraper.
Continuity mistake: When the Soviet missile is about to be launched, the sky changes from daytime to dusk.
Continuity mistake: Before Nuclear Man burns Luthor's dollar bill, Luthor looks to his right, immediately after, the shot from behind shows him looking straight forward.
Continuity mistake: During the volcano scene, a girl is holding on to the priest's arm at wrist level. A split of a second later her grip changes to above the elbow level.
Continuity mistake: When the window shops explode, the grey car close to them disappears in the following shot.
Continuity mistake: When Superman rescues Lucy in space she is placed on his right side. A frame later she is on the left.
Continuity mistake: In the hotel suite, the kitchen door is always open, except for the moment when Superman has to look through it, when the door appears magically shut.
Continuity mistake: When Nuclear Man flies through the Daily Planet floors, the last place he breaks into has the exact same decoration as Lex Luthor's penthouse, despite the fact that in previous scenes we saw that Luthor lives in a totally different building.
Continuity mistake: In the beginning of the UN sequence, we see a brief outside shot of the real UN building, but the further shots of the fake building have none of the elements from the shot we just saw: Flags, white stone wall.
Continuity mistake: When Superman is entering the UN, an Arab man greets him and turns his head around from right to left. In the following closer angle he repeats the movement.
Continuity mistake: The SWAT people that are falling off the truck when it gets lifted disappear in the next angle where we see the pavement and a close up of the front of the truck.
Continuity mistake: When the window shops explode, a taxi cab door is widely open to show a Budweiser ad on it. In the following wide angle from above the door is closed.
Continuity mistake: Nuclear Man watches the Daily Planet paper with the "New publisher for your favourite paper" headline. The first shot shows the paper slightly wrinkled on the left and bent to the right. In the following angle it is straight and perfect.
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.