Continuity mistake: After the "Drop dead" cover, Jimmy Olsen talks to Lois. In the close-up of Lois while she says "He looks like my father," the journalist behind her is standing up. An instant cut later, he is seated.
Continuity mistake: When Nuclear Man steals the Statue of Liberty, its pedestal looks normal. When Superman puts it back in place, the pedestal is missing a huge chunk (surely because of some FX going wrong). In further shots, it's fixed.
Continuity mistake: When Moscow's Red Square scene begins, the tanks and soldiers parade in front of the authorities (a combination of matte painting and a real set). When Superman arrives, a second tree has appeared next to the one on the left. On the right side, an unfinished painting has replaced the previous huge wall, trees, and decor. (International theatrical, TV, and LaserDisc releases).
Continuity mistake: Before Nuclear Man finds the newspaper with Lacy's photo, he is at Lex's lair kneeling down, then starts to fly. Big clouds of smoke come out of his wrists, but an instant cut later in the close-up, the smoke is gone.
Continuity mistake: At the hotel room, when Superman rushes and leaves, Lois runs towards the window. A shot later, she is gone, only to reappear an instant cut later.
Continuity mistake: When Superman and Lois end their flight, her legs are stretched down, about to land on the ground. An instant cut later, they're bent, and she is lowering her legs again.
Continuity mistake: When Lois drives to the UN Lacy is not in the car. Half a second later she appears inside.
Continuity mistake: When Superman flies to save the girl inside the tornado and the family exits the basement there's a truck by the entrance door filled with hay. Half a second later the truck is gone and reappears behind the family, but now it's empty. (Laserdisc and international extended editions).
Continuity mistake: When the movie begins, the cosmonaut has some sort of big compass attached to his legs that disappears in the wide shots.
Continuity mistake: Lex is a bald man, except for this movie where he has very obviously natural hair.
Continuity mistake: After Superman ducks the moon rock, there's a close-up of Nuclear Man's black boot stepping on Superman's boot, yet in the next angle, it's Nuclear Man who's yelling in pain. It should be Superman instead.
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.