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These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Awesome Music: Unlike Superman II and Superman III, this has a substantial amount of original music; John Williams didn't score this one - his longtime friend and regular orchestrator Alexander Courage did - but he did write new themes (for Jeremy, Lacy Warfield and Nuclear Man).
Then again, this is kryptionian hair we are writing about...
"Funny Aneurysm" Moment: A particularly horrifying example, where Clark Kent goes to a gym with Lacy Warfield and pretends to injure his back lifting weights. It's not a direct parallel, but the image of Christopher Reeve holding his spine and wincing in pain is very eerie.
So Bad, It's Good: Superman IV is arguably funnier than Superman III; it has Narm in spades, and Unintentional Comedy > Failed Gags every time.
The mere presence of Gene Hackman can make anything a little better, and his Ham and Cheese here, as both clever Lex Luthor and the voice of all-brawn, no-brains Nuclear Man, is quite tasty. Jon Cryer's Totally Radical Lenny Luthor is more bearable than it otherwise would have been with Hackman to play off of.
Special Effects Failure: A human woman breathing perfectly finein space, as it was originally intended for her to be in the skies above Metropolis. There's plenty more where that came from — poor compositing, Superman "rebuilding" the Great Wall of China...even the opening titles are crap!
Don't forget that, infamously, just about every shot of Superman flying is the exact same shot.
Surprisingly Improved Sequel: As horribly received as the film was on its initial release, many have come to regard this as a better sequel than Superman III in more recent years, due to the fact that this film at least took itself relatively seriously and tried to have a genuine (if hamfisted) message rather than the buffoonery that made up most of the previous sequel. Few people actually claim it to be good, mind, but it does get a lot of slack that III doesn't.
Took the Bad Film Seriously: Christopher Reeve had to have known that the Superman film franchise was on its last legs when he signed up (with stipulations) for Superman IV: The Quest For Peace. To note, Reeve would only take the film if several conditions were met, one of them being a strict anti-nuclear message. While other members of the cast understand how bad the script is (Gene Hackman was there for a check and Jon Cryer was camping it up), Reeve gives it his all and delivers the only emotionally honest performance in the film, which is especially evident in the scenes where he prepares to sell the Kent family farm, and the sequence where he delivers a stirring speech to the United Nations. It's enough to make the viewer wish that the film wasn't screwed over with the most ridiculous villain ever seen in a comic book film (Nuclear Man).
What an Idiot: Apparently, no one in Metropolis bothered to install dead-man switches into their subway trains.