Factual error: If the Russian cosmonauts need special suits to survive out in space, so should Lacy when she is abducted by Nuclear Man. (00:02:50 - 01:20:20)
Factual error: When Superman addresses the UN, the delegate presumably representing the United Kingdom appears behind an "England" sign - "England" is not an international entity represented at the UN, while the United Kingdom of Great Britain and Northern Ireland is. (00:32:20)
Factual error: Superman places the nuclear missiles in the giant disposable bag in space, throws them at the sun, and the bag burns up when it hits the sun. In reality, the bag would have burned up long before hitting the sun. (00:35:35)
Factual error: Superman and Nuclear Man fly around the world fighting at incredible speed. Everywhere they go, including places as widely spread as New York and China, it's daytime.
Factual error: While in space, Superman and Nuclear Man's capes are flapping. Since it is a vacuum, there is no air, therefore the capes shouldn't flap. Likewise, on the moon, the dust and dirt are moving too quickly to be in a micro gravity situation.
Factual error: At the beginning of the movie we're told that the Statue of Liberty is in Metropolis. However, the subway billboard states that it's in New York.
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.