Continuity mistake: When Superman leaves the farm, after the tornado, the basement doors swap from closed to opened between shots. (Laserdisc and international extended editions).
Continuity mistake: No soldiers are visible in the aerial angle of the Russian parade, but dozens in the immediate close-up. (Laserdisc and international extended editions).
Continuity mistake: When Superman blocks the Russian missile during the parade, its position keeps changing in every single shot. Sometimes it's close to the politicians, others away... This changes back and forth. (Laserdisc and international extended editions).
Continuity mistake: When Nuclear Man bombs the Russian truck during the parade, the politicians are standing apart, calmly. A frame later they are squeezed together horrified. This keeps changing half a dozen times. (Laserdisc and international extended editions).
Continuity mistake: When Jenny is about to be sucked by the tornado, the windows are banging violently. The shot changes to a wide angle of her flying away and the windows are opened wide and still, despite the tornado blowing. (Laserdisc and international extended editions).
Continuity mistake: The floating pliers behind the cosmonaut keep appearing and disappearing between shots.
Continuity mistake: The cosmonaut is fixing a satellite dish with his left arm but a frame later he's working with his right arm instead.
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.
Continuity mistake: On the moon, Nuclear Man grabs a rock and dirt covers him totally, especially his armpit becomes black. A frame later, he's spotless.
Continuity mistake: When the volcano's lava floods the village, there's a wide shot of the mountains and the volcano and you can see that the lava is still running down the volcano, not near the village.
Continuity mistake: When the firemen are about to grab the hose and it explodes, note that the other hose inside the truck on the right side has changed positions between shots.
Continuity mistake: Nuclear Man walks towards the newspaper where Lucy's picture is, for a brief moment there's a light smoke coming from behind him as if something was burning (it has nothing to do with the smoke Nuclear produces when flying) which is later gone (according to SupermanIV.com a deleted scene involved Nuclear Man waking up, "he sees and picks up the newspaper with Lacy, which then catches on fire in his hand.").
Continuity mistake: Before Nuclear Man see Lacy's picture in the newspaper, he rises from the floor and a wide angle reveals that the table is nowhere around, yet a couple shots later it simply appears half a meter away from him.
Continuity mistake: When Lois visits sick Clark she stands by the door, fully lit, a frame later, when the angle changes, the whole place is in the shadows.
Continuity mistake: When Superman first meets Mr Warfield, the orange pencil on the table changes positions between shots.
Continuity mistake: When Superman stops the train there are two thick black tubes next to the tunnel behind which disappear when he leaves.
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.
Continuity mistake: When Superman throws Nuclear Man down the power plant, Nuclear's black wristbands disappear and reappear between shots.
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.