Continuity mistake: When Superman flies to save the girl inside the tornado and the family exits the basement there's a truck by the entrance door filled with hay. Half a second later the truck is gone and reappears behind the family, but now it's empty. (Laserdisc and international extended editions).
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.
Revealing mistake: When Superman discovers that Nuclear Man is stealing the Statue of Liberty, he turns around and you can see the wrinkles on his temple from the wig he was using.
Visible crew/equipment: After Superman leaves Lenny in school, he takes off and the wooden barrier of the platform ascending him is noticeable on the lower left side of the screen.
Visible crew/equipment: When the SWAT van is lifted up there is a crane reflected on SWAT van.
Revealing mistake: After Superman leaves the Statue of Liberty, a thick string is noticeable under his cape to keep it up and fluttering.
Revealing mistake: When the missile is launched, Superman flies to catch it. However, his face has some sort of stocking over the upper part and the man looks nothing like Christopher Reeve. It was either a stunt double, a bad special effect, or a cheap mannequin.
Visible crew/equipment: When the cosmonaut is fixing some cables, a crew member's hands holding the camera are reflected on his visor.
Revealing mistake: When Nuclear Man's fingers hurt Superman's nape, part of the Statue of Liberty's tablet disappears.
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.