I would say that Superman III and IV could have been fixed with little effort.
Okay, to fix Superman III, the first thing I would do is ditch Richard Pryor, evil Superman, and the comedy. That would fix about 90% of the film right there.
Supposedly, the supercomputer in the film was originally going to be called "Brainiac", so I would add that back in. Then I would just take the events of the movie and tweak them a little.
Now you have Robert Vaughn as the evil CEO Ross Webster who recruits a naive computer genius (formerly Pryor's character but now played straight) to build a supercomputer called Brainiac.
Like in the film, Webster's goal is merely to use it to manipulate financial markets. However, Brainiac becomes self-aware and starts to take control of the world's computers. When Webster tries to shut it down, Brainiac transforms him into a cyborg (as it did to Webster's sister in the film). Furthermore, it also transfers it's mind into Webster, so we have a humanoid Brainiac like in the comics.
Now, as to Superman IV, I would drop the "get rid of all the world's nuclear weapons" idea and focus on a smaller nuclear issue.
I would have Lex Luthor manipulating two small Eastern European countries that are on the verge of war. Unbeknownst to either, Luthor is promising them each a nuclear weapon. What they don't know is that he is really using the nuclear material (combined with Superman and Luthor's DNA) to make Nuclear Man.
My version of Nuclear Man would gain his powers by absorbing radiation. The material he absorbs turn to lead.
With Nuclear Man finished, Luthor uses him to conquer both countries. He then sends him out to defeat Superman, which he does.
Now Nuclear Man starts getting idea's of his own and doesn't feel he should share his power with Luthor. He has Luthor tossed in the same dungeon as the wounded Superman.
Luthor helps Superman escape and they make it to Lex's lab where exposes Supes to solar energy, which heals him. He also gives him a secret weapon he's been holding on to.
Superman confronts Nuclear Man. Superman is winning because Nuclear Man's energy is starting to run down. When Superman "accidentally" lets slip that Lex has some highly radioactive material in a lead case, Nuclear Man heads for it, rips open the container, and absorbs the contents.
The radioactive material turns out to be Kryptonite.
Nuclear Man feels more powerful than ever. However, he begins to turn green and starts feeling sick. Eventually, his body turns to lead.
Superman restores the proper leaders to their place and is on hand as they sign a peace treaty. Superman goes to place Lex under arrest, but Luthor points out that Supes doesn't have any authority here.
Luthor doesn't gloat for long because the countries leaders place him under arrest. When Lex realizes they have the death penalty, he begs Superman to take him back to prison. The leaders agree and Supes picks up Lex and flies off.
Of course, part of the problem with Superman IV is that they ran out of money and were stuck with crappy effects, so I'm not sure my version would necessarily be better...