Having cake and eating it beforehand
At the end of the first Superman movie, our hero is faced with the dilemma of either saving a whole town, or saving Lois Lane. Spoiler alert: He does both. But how he does it is interesting.
First he saves the town. Then he rushes off to save Lois, but Tragedy! He's too late, and she's dead. So he flies up into space and starts whizzing round the world.
He is not making the planet spin backwards, as some people seem to believe. That would be stupid. He's just accelerating past the speed of light, which causes him to go back in time, which makes it appear that everything else is going in reverse. I don't know why this is confusing. It always seemed obvious to me.
Anyhow, he's gone back to the point where Lois hadn't died yet and rescues her. Yays all around.
the question that I don't think is ever addressed is; does this mean that he now hasn't saved the town? Has him appearing in the past overwritten the previous timeline? Or are there now two Supermans at this point in time? And if so, what happens to the spare?
For the sake of argument, let's say that the Superman who saves the town goes back in time to save Lois, even if she has already been saved before he leaves. That way there is only ever one Superman, it's just that his timeline is a bit tangled.
Of course once you've established that you can always fix stuff later, it all gets a bit Bill and Ted, except worse. Bill and Ted time travel never overwrites an incident, it just allows our heroes to decide to have done something, and then subsequently go back in time to actually do it. They don't cheat. Ted's dad's keys are missing in the movie long before B&T decide to take them, so they will always have stolen them. The timeline is not changed. When Superman goes back in time he adjusts the timeline so events happen differently.
Which means that not only can Superman go back and change any event he doesn't like, he can be in several places at once. He can oversleep, and then go back in time and still get to work on time. He can be defeated by Lex Luthor, but so long as he escapes afterwards to go back in time, he can get a do over until he gets the best outcome. If necessary he can go back and destroy Luthor's Big Zappy Gun of Doom and at the same time defeat Luthor himself at a different location, and also stay home to watch the Superbowl, if it happens to clash and he's into sports.
The downside is that he ages at the same rate, whether he's going backwards or forwards in time, so if he overdid this kind of thing he'd getting older than everyone else because of all the side-trips he was making, but Superman doesn't seem to age at a normal rate so it probably wouldn't show. It might also get a little confusing after a while, so I imagine his To Do list would get complicated.
1) it's been a long time since I've seen it, so the details elude me.
2) Though you'd think it would be difficult to fine tune how far back you went at that kind of speed, even for the Man of Steel.
3) And let's not think about the original timeline, where she isn't saved, that sets the whole thing up.