I find myself charmed by Superman III despite the flimsy nature of the film. It seems to stand astride two basic foundations, one the foundation laid down by the original Superman films, and the other by the 80's and what the suits wanted. As you can guess, these didn't go together well at all.
I'll just rattle away a bit, so excuse any rambling.
I found myself most charmed by the computers. Despite the fact that they really didn't act like computers at all, because the writers were pretty ignorant of computers of the day, they only had period computers to work with, and all the misconceptions about computers were period misconceptions, only workable in that period. We saw green screens, amber screens, keyboards, tape reels, and all other sorts of stock computer tropes, all slightly updated for the 80's and the personal computer revolution.
Not surprisingly, the big villain turned out to be a computer created by the supposed big villain (who was Not-Lex-Luthor and Not-Lex-Luthor's evil sister). This computer became self-aware, seized the evil sister, and turned her into a cyborg to fight Superman. I can't say that this is the first film that depicted the fear of computers taking over, but it certainly brought the subject out of the cult sphere and into mainstream conciseness. Computers strip away our humanity.
In that way, I suppose that S3 had the theme of humanity being stripped away, and without that, we become cruel. There's a place where Superman is split in half to fight his evil self. His human self is the part that wins, not his super self. It is then this human-superman that defeats the evil computer by using his human smarts. Despite their seeming divinity, computers, not matter how well programmed, are not our new gods, for even if they are all powerful, they cannot be all knowing.
This is re-emphasized with the updated Lana Lang, a "today's girl" who's a level-headed single mother struggling to raise her son well. She's got her act together, not like the flighty or defenseless women of previous decades, but also not aggressive, like Lois Lane. Her Superman is not a man who flies around with a cape, but a man who comes home and helps her to make a family, which makes Clark quite the Superman indeed.
What is humanity? Family. Middle-American values. Sober living. Sweaters draped across the shoulders and conservative dress. All the stuff that makes the Moral Majority happy. (There would be no more Superman bopping Lois Lane in the 80's).
The first two Supermans were products of the Carter era, or more importantly, the Post-Nixon era, where our icons have fallen and we really do need a new icon to stand up for America. In the 80's, we are now into the Reagan era, the Conservative have come into power, and the center of symbolism has changed.
The new villains are Corporations, not dictators, and their limitless ambition only worships at the altar of money. We saw this begin with Lex Luthor's in the first Superman, but then he was just this guy with an evil plan. This time, the villain leads and entire corporation. Out in the real world, this is an era when corporations are always changing their names (or so says Jefferson Starship), merging, and synergizing. Old corporate names are literally disappearing as new ones emerge, moving factories to other countries, and playing a new kind of economic politics to their own advantage.
The film makes strides against racism. I don't think that we saw a single black face with a speaking part in the last film, but in this one, the co-star is Richard Pryor, a black man. We also see a black fire chief amid a sea of white faces. Even so, the majority of all faces remain white and male.
The actual plot of the film is rather ridiculous, even by Superman standards, with an weak overall ending. The main villain creates fake kryptonite, which turns Superman evil, then splits him in two, but after he literally pulls himself together, flies off to defeat the evil computer which has run out of control. The story feels like a modern Hollywood film, where someone wrote a decent script, and then suits demanded changes until the whole film rattled along, good-enough, but not great. Honestly, I can't stay that it's any more incoherent or stupid than the latest X-Men film.
What missing from the film is everything 80's. If you will, this film depicts an idealized 80's, with no modern music, new wave fashion, punks, Japanese cars, smog, or anything else rejected by middle-America. In a way, the film de-urbanizes Superman, saving him from the East-Coast elites. It's only his return to middle-America that reconnects Superman with his White Christian American roots, that makes him a truly American again.