The movie's original budget was $36 million. Just before filming was to begin, Cannon Pictures, which was experiencing financial problems, slashed the budget to $17 million. As a result, the filmmakers cut corners by doing things like reusing 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 a number of serious special effects errors. The deleted footage was considered for a fifth Superman film.
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."
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 the director run the camera in reverse rather than a complicated super-speed scene.
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 "Superman IV".
The Cannon Group, thinking that they had a potential blockbuster on their hands, cut the two-hour-plus film down to a lean 90 minutes so that theater owners could have more screenings per day, and potentially make more money that would eventually filter back to the studio.
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.
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 civilians, 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).
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 20". Superman and Lex wouldn't appear in a feature film together until 19 years later, in Superman Returns.