Continuity mistake: When Superman and Nuclear Man fight on the balcony the high powered binoculars disappear.
Continuity mistake: After smashing his head, Superman sends Nuclear Man flying away. At first, Nuclear Man is conscious and with his head pointing upwards. A frame later he is unconscious and the head is laying down.
Continuity mistake: Before Clark steps down off the trolley, a group of people surrounded by suitcases are seen on the back, but disappear when the angle changes.
Continuity mistake: When Nuclear Man is destroying Metropolis, the same stuntman with a gabardine and a hat is seen close to a shop window, then a second later in the middle of the street and a second afterwards getting thrown through the air with a group of people. He looks and dress just like Clark Kent, guess it's his stand in doing some extra work.
Continuity mistake: The Statue of Liberty manages to fall down straight the whole long time, but when it is is about to hit the ground, the angle changes and the statue has magically tilted sideways.
Continuity mistake: When Superman falls straight and unconscious off the Statue of Liberty he's facing a 9 o'clock direction. In the next angle he is facing 5, then lands facing 7.
Continuity mistake: When the lava is flooding the village, a big green plant appears close to a priest. When Superman cools the lava and the smoke goes away, we see that the plant is much smaller and less leafy.
Continuity mistake: When Superman takes off after saving the boy in the Great Wall of China scene, you see him heading up, as if leaving, but in the next cut, he's on the ground next to the wall.
Continuity mistake: Lex's fat assistant enters the place with the missiles' control panels. Outside he is seen entering through an open door. From the inside, the door is closed and he enters a second later.
Continuity mistake: When Nuclear Man lands on Metropolis a cop on the right is opening the door of his car. In the next shot he is repeating the movement.
Continuity mistake: When Nuclear Man arrives to earth, full of energy from the sun, his footsteps don't glow; neither do they when he arrives to the balcony, several scenes later. Then a couple of seconds after they glow but stop glowing when he walks towards Superman and keep that way for the rest of the film.
Continuity mistake: When Superman is taking the missile with the rest of the weapons, its colour changes from dark black to light grey.
Continuity mistake: During the volcano eruption the animal on the right (goat or sheep, I don't know) keeps changing from brown colour to white.
Continuity mistake: When Superman throws the rock into the volcano, it flies from right to left into a huge cloud of smoke. In the following angle, it is falling from the blue clear sky, up away from the smoke.
Continuity mistake: When the volcano erupts, a wide shot shows a group of people behind the cop and the priest. In the following shot a woman appears in front of the cop.
Continuity mistake: After the SWAT van is lifted, it tilts forward. A frame later, it's looking sideways.
Continuity mistake: The cab's hood, crumpled by Nuclear Man's power beam, magically smoothes itself a frame later.
Continuity mistake: The rock that hits the prop-astronaut blows his head off. Seconds later the head is back in place.
Continuity mistake: Lois visits Clark and takes her coat off, folds it and places it on her arm. A frame later the coat is lying on the couch.
Continuity mistake: When Clark is about to enter the subway train, the people by the door appear and disappear all the time: A cop, a man with a hat, a lady in a leather jacket.
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.