Jason's "asthma" is really his half-Kryptonian physique trying to adjust to Earth's environment. Since Lois didn't know he was Clark's (yet), she took him to Terran physicians, whose treatment abated some of the symptoms. Later, when she was threatened, his natural abilities manifested themselves, purely on reflex. And only then did she realize who's the real father.
The 'S' on Superman's chest looking more like a shield suddenly made his ability to show the 'S' at Non in Superman II much more sense.
Jimmy Olsen mentions how Lex Luthor was able to escape prosecution for his crimes thanks to Superman's absence during his trial. What about the rest of the witnesses to his plans to destroy California or his alliance with Zod? Well, Zod and his retinue were killed by Superman, Lois got her memories wiped out by Supes and Eve Teschmacher is never seen again after visiting the Fortress with Luthor. So yeah, Superman was the sole witness available...
Though this puts into question why the court couldn't bring Otis in to testify against Luthor, considering that Luthor and Otis parted under not so "friendly" terms in Superman II.
In other continuities, Kryptonite radiation is poisonous to humans who are exposed to it for a long time and it's never been stated it isn't in this one. Had Superman not taken the Kryptonite continent away from Earth, Lex would have doomed himself and everybody else living in it to a slow and painful death.
Though the earlier movies were made when it was canon that Kryptonite only affects Kryptonians. So unless Backported Development is involved, then the only thing humans had to worry about was the Kryptonite continent growing until it destroys much of North America and parts of Europe.
When it was announced that Brandon Routh would reprise the role of Superman for Crisis on Infinite Earths, specifically the Kingdom Come version, people assumed it was a separate Clark. Then Marc Guggenheim clarified that it was indeed the version from Returns.. and since the Returns!Clark IS the Reeves!Clark...
Fortunately, the deaths of his wife and everyone else at the Daily Planet were undone, thanks to Oliver restoring the Multiverse.
