Audio problem: On the moon, Superman smashes Nuclear Man's head against his knee. The clonk is heard before the hit (even forgetting that sound can't be heard on the moon).
Audio problem: When Lenny drives his car into the quarry, the sound of his radio changes depending on where the car is; but when he drives away, suddenly it stays constant. It should have decreased, and increased when we get to the close-up.
Audio problem: When Lex is giving instructions to launch the missile, a young man puts on his earphones and talks to Lex, but his mouth doesn't move.
Audio problem: When Nuclear Man knocks out Superman on the moon we hear some growling, but their mouths aren't moving.
Audio problem: When Nuclear Man puts Lenny down on the floor, Lenny babbles some things but his mouth doesn't move.
Audio problem: When Superman is wounded on the neck, and when the italian villagers are saved, the same male falsetto voice is used to add a (crappy and out-of-sync) "Oooh!" and "Aaaah!".
Audio problem: When Lois and Clark jump off the terrace, she cries his name. In the wide angle she moves her mouth but no sound is heard.
Audio problem: After the satellite crashes against the cosmonaut, inside the spaceship a Russian cosmonaut starts to cry out things, but his mouth isn't moving.
Audio problem: When Lex enters the military bunker, officer Goram's voice is obviously dubbed and sometimes the audio doesn't match his lips.
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.