Revealing mistake: When Lenny's car, with the cops in it, flies into the air you can see it's empty.
Revealing mistake: When nuclear Man shoots at the cops, the scene is being played backwards.
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.
Revealing mistake: When Lois and Superman are flying together, they turn green, specially Lois's arms and hands.
Revealing mistake: Outside the UN, a woman in a red coat appears behind the hot dog stand and when the angle changes to the opposite side, in front of her, she's also there.
Revealing mistake: During the tornado, when the little girl cries by the window check the lower corner of the window on the right and you'll see the white string moving the window. (Laserdisc and international extended editions).
Revealing mistake: Right after Lex, disguised as a soldier, orders the launching of the missile, there's a shot of the truck carrying it. The driver is a cheap mannequin that looks very much like a scarecrow.
Revealing mistake: Due to the blue-screen effect, part of Superman's glasses disappear when he is free falling with Lois.
Revealing mistake: Watch the cars and the grey truck during the LexTv scene. Whenever Luthor appears on screen the same cars are driving on the street.
Revealing mistake: It is way too obvious that when Luthor holds the dollar bill, his arm and hand have been replaced by a robotic prop. His arm manages to move without involving all the bones connected to the shoulder and the back.
Revealing mistake: While Superman carries the Statue, there's a close shot of Nuclear Man showing his fingernails. The movie behind is playing the wrong way, and gives the sensation that Nuclear Man is flying backwards.
Revealing mistake: The close shot of people panicking when the Statue is about to crash against the pavement shows an old woman with a red wool hat and a white scarf. Many scenes later, when Nuclear Man lands on Metropolis, the same lady is seen, wearing the same clothes.
Revealing mistake: When in space, Superman punches Nuclear Man on the back, he turns around and his face has turned blurry and black, but his body keeps the same colour. In the immediate close-up the face's colour is fixed.
Revealing mistake: The elevator cables that Superman holds should be greasy, or at least dirty, but they are not, revealing he's merely holding a black rope.
Revealing mistake: After Nuclear Man rampages Metropolis, Superman cries "Stop!" and a SWAT agent descends from the sky on visible wires.
Revealing mistake: While Nuclear Man and Superman are falling off the balcony, their skin switches from pink to natural. When Nuclear Man finally flies away he loses all of his colour and becomes semi transparent.
Revealing mistake: While flying with Lois, Superman lets her go and when he picks her up all of the wires holding him are visible.
Revealing mistake: When the volcano erupts, it's obviously a painting because the lava doesn't flow or move an inch.
Revealing mistake: When Superman returns the cosmonaut back in the spaceship, Superman's head becomes transparent, and the cosmonaut's helmet becomes wobbly, all because of the use of blue-screen.
Revealing mistake: After Superman sets the Statue back in place, he lands on the ground and the wall behind wobbles, revealing where the movie was retouched to hide the wires.
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.