Old Shame: Christopher Reeve felt so ashamed about this movie that he swore he'd never play Superman again. It took lots of persuasion to bring him back for Superman IV, which sadly didn't turn out much better.
Promoted Fangirl: Annette O'Toole admitted in an interview for the documentary Look, Up in the Sky! that she loved reading Superman comics as a child, and preferred Lana Lang to Lois Lane.
According to Ilya Salkind, the original script was going to involve Brainiac and Mr. Mxyzptlk (who would have played by Dudley Moore) teaming up against Superman, who would also meet his cousin, Supergirl, who was adopted by Brainiac.
The original title for the film was going to be Superman vs. Superman.