Richard Donner, who'd been fired from Superman II (1980), was offered the director's chair; he declined. Donner, at the time who was originally directing the first two Superman movies, was planning to make and produce at least four Superman films.
The movie's original budget was 36 million dollars. Just before filming was to begin, The Cannon Group, Inc., which was experiencing financial problems, slashed the budget to seventeen million dollars. As a result, the filmmakers cut corners, by doing things like re-using special effects.
Christopher Reeve's flying harness was concealed under a larger version of the red shorts he wore for the costume, making his waist look bigger. In previous Superman movies, the bigger waist was hidden by the cape, quick cuts, or creative camera angles. In this movie, the bigger waist is clearly visible, leading some reviewers to speculate that the thicker waist was Reeve's actual waistline.
Originally, the film had two Nuclear Men. The first, dubbed Nuclear Man 1, wore a black costume. His scenes were filmed, but eventually cut, allegedly because previews revealed several serious visual effects errors. The deleted footage was considered for a fifth Superman film.
The Cannon Group, Inc., thinking that they had a potential blockbuster on their hands, cut the two-hour-plus film down to a lean ninety minutes, so that theater owners could have more screenings per day, and potentially make more money that would eventually filter back to the studio.
In the original script, Superman was supposed to rebuild the Great Wall of China at super speed, but when money problems emerged, they had Superman use his "magical rebuilding power" (which had been completely made up for the film). It required only that Director Sidney J. Furie run the camera in reverse, rather than a complicated super-speed scene.
Supergirl (1984) is not mentioned anywhere during the film. The spin-off film was released between Superman III (1983) and this film. Christopher Reeve was originally going to make a cameo in the film, but passed.
Before Superman IV: The Quest for Peace (1987) was released, The Cannon Group, Inc. began planning a fifth film, directed by Albert Pyun. When Cannon went bankrupt, Superman's film rights reverted to Ilya Salkind and Alexander Salkind. Ilya wrote a story for a fifth film with Cary Bates and Mark Jones, in which Superman died, and was resurrected in the bottled city Kandor. It was not an adaptation of the famous "Death and Return of Superman" storyline, which it predated by about two years.
The shots of Superman using his "wall rebuilding vision" to repair the Great Wall of China, are just re-purposed footage of him waving at the people, in fact it's the same shot used twice, with it being mirrored the second time to hide the fact that it's repeated (this is apparent from the parting in Superman's hair switching sides between shots).
When Superman makes his speech at the end of the film, he paraphrases Dwight D. Eisenhower when he says, "there will be peace when the people of the world want it so much that their leaders will have no choice but to give it to them."
At the end of the film, Superman says to Lex Luthor as he's dropping him back off in the prison quarry, "See you in twenty". Superman and Lex wouldn't appear in a feature film together until Superman Returns (2006).
Tom Mankiewicz, creative consultant for the first two Superman films, was approached by Christopher Reeve to pen the screenplay for Superman IV: The Quest for Peace (1987), but declined the offer. He did however, made the suggestion for this film, that Superman must deal with a human conflict that even his superpowers can't control, which formed the basis of Superman challenging the nuclear arms race.
No soundtrack release to this film was released for over twenty years until Film Score Monthly issued an 8-CD box set called "Superman: The Music (1978-1988)", which presents the complete score to this movie.