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.
Revealing mistake: When nuclear Man shoots at the cops, the scene is being played backwards.
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.
Continuity mistake: In a split second, all of the snow on the mountain cut by Superman disappears.
Continuity mistake: When Superman saves the falling woman at the Great Wall, he flies in a 1 o'clock direction. A frame later he is positioned in a 12 0'clock.
Continuity mistake: When Superman stops the Soviet spaceship from turning around the solar panel is facing upwards, a second later the spaceship has changed position and the panel is sideways.
Audio problem: When Nuclear Man puts Lenny down on the floor, Lenny babbles some things but his mouth doesn't move.
Continuity mistake: When Superman lands near the UN, Lois and Jimmy disappear from the crowd, only to appear half a second later, in the closer angle.
Continuity mistake: The Soviet missile has legible CCCP red letters, but in the following shot it's covered in snow, although the close-ups don't show any snow falling.
Continuity mistake: Outside the UN, the hot dog in the kid's hand suddenly disappears.
Continuity mistake: Superman is on the moon, about to cause the sun eclipse, and flies to the left, as if he were to exit the moon. In the next shot Superman is seen coming from the void towards the moon again.
Continuity mistake: When Lois is packing Superman's cape and Lacy says "I had nothing to do with it", there's no continuity with the passers-by seen behind. A kid in a red t-shirt, for example, appears from nowhere.
Continuity mistake: When Superman saves the girl from the Great Wall of China and starts rising, a woman with a white hat behind lifts her arm to say goodbye. In the following angle she is repeating the movement.
Continuity mistake: Before nuclear Man lands in the city, there's barely any smoke. A split second later, the close shot is completely filled with smoke. Then it disappears when we see the old lady with the yellow bag, and reappears when we go back to Nuclear Man.
Revealing mistake: In the aerial shot of Nuclear Man entering the crater of the volcano the smoke coming from it is still, thus revealing it's a painting.
Continuity mistake: While Superman is in awe reading the "Drop dead" headline, there's a group of journalists on the background and an empty chair on the right. When Clark stands up, a man appears seated on the chair.
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.