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).
Character mistake: When the little girl is about to be blown away by the tornado she is crying terrified, but when she is swallowed by the tornado, spinning around violently, she stays totally calm, even bored. (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).
Revealing mistake: All of the shots of Nuclear Man flying, or him turning around to check for Superman are the same ones repeated over and over again.
Revealing mistake: During the tornado scene, the wind makes the windows open and close violently, but the cowboy hat on the porch stays in place barely moving. (Laserdisc and international extended editions).
Character mistake: The Daily Planet newspaper headline "New publisher for your favourite paper" has "favourite" is spelled the British English way. Since Metropolis is in the United States it should be spelled "favorite."
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.
Other mistake: When Lenny has the prison guards locked in the car and is putting the top up, the steering wheel is spinning but the front wheels aren't moving. The amount of revolutions of the steering wheel is mechanically impossible also.
Revealing mistake: When Lacy floats in space, Superman saves her and heads towards Earth. When he comes back, the shot of the Earth behind is the same one from before, yet reversed.
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.
Other mistake: When Lois and Superman fly together, the part where they fly over some horses is the very same shot as when they fly over the Golden Gate for the second time.
Other mistake: When Superman breaks his ice cage and makes it explode, a long black rubber band flies away. Where the heck did that come from?
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.
Revealing mistake: When the volcano erupts and lava floods the village. The red truck on the left is a very obvious scale model prop: The engine is missing and the hood is attached to the grilles.
Revealing mistake: When Nuclear Man melts the rifle, note that the SWAT member is holding the barrel and he slides his hand away slowly to make the barrel bend downwards. He was obviously holding it up. If he had burned himself he would've moved faster.
Revealing mistake: When the fire truck explodes, note a tube behind it going straight to the truck. Probably an FX device to effect the smoke.
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.
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.