The beauty of the Elseworlds concept from DC Comics is that it allows writers and artists to tell stories outside of the constraints of existing canon. Sometimes, this produces something magnificent like the Alex Ross classic Kingdom Come. And other times, the results end up being proof that if it's not broke, it probably doesn't need fixing.
There have been a lot of Elseworlds stories over the years and not all of them make sense, even inside the concept of changing things up. Sometimes, the idea can stray so far from the core concept it no longer makes sense.
10 Superman/Wonder Woman: Whom Gods Destroy
Any story that features Superman as an evil, drunk centaur is going to have an uphill battle in the logic department. The idea behind Whom Gods Destroy never really coheres, which is a shame considering it's from Chris Claremont, who changed the X-Men forever. In Whom Gods Destroy, the Nazis won and Wonder Woman is one of them. This alone invalidates the entire concept, as do questionable choices (like turning Superman into a centaur, because why?). Lois Lane becomes Wonder Woman to defeat evil Nazi Diana but by then it's too late.
9 Holy Terror
The first official Elseworlds title - the first to bear the Elseworlds logo, at least - doesn't get things off to a good start. In Batman: Holy Terror, America is ruled by a theocratic government and Bruce Wayne is a priest. He discovers that the government may have been behind the deaths of parents, and he becomes Batman, or kind of. One reason it doesn't really make sense is that religion has never been featured in Batman's mythos otherwise. He's a remarkably agnostic character considering his near-fanaticism, but placing him in this scenario didn't really work.
8 Guardian Of Gotham
Within the comics, it's a consistent trope in Elseworlds to put someone else beneath the Batman cowl. It was inevitable Catwoman would get the chance. That said, Guardians of Gotham doesn't really make sense. Nothing is really different the actual Batman is a murderous psychopath. Well, Two-Face is a woman (an option for the next big-screen interpretation of him). Otherwise, the story is very 90s which means it emphasizes shock and awe (and the male gaze) over internal narrative logic. The story never really goes anywhere.
7 The Nail
The Nail was strange because it was just boring. Sometimes a creative team can go too far in Elseworlds. Sometimes, it's not far enough. The story is basically what happens if there were no Superman. The titular nail is one that flattens the tire of the Kents before they can find a baby Kal-El in Kansas.
The Justice League exists, but they're outlaws thanks to the efforts of Lex Luthor. None of it really makes sense given what fans know of the characters and their motivations.
6 At Earth's End
At Earth's End spawned one of the most unintentionally funny Superman memes of all time. For some reason he felt compelled to scream "I AM A MAN!" and that's about as much sense as this story makes. This story gets in early on the 'old man' trope (like Marvel's Wolverine) currently very popular in comics by showing an older Superman in a post-apocalyptic world. There are biker gangs because there are always biker gangs and of course Nazis. Despite being Superman, he solves the problem with lots of guns.
5 Act Of God
This limited series by writer Doug Moench has all the superheroes on earth lose their powers due to an unexplained event. A few maintain them. The real problem is this 'act of God' never accounts for the fact that not all superpowers derive from the same source. Some characters come by them by an accident of fate, genetics (like Superman and Martian Manhunter), or some kind of mysticism (as was the case with Wonder Woman, at the time). The logic of it never made sense.
4 Created Equal
Created Equal shares a lot in common with the core idea of Y: The Last Man (a television adaptation is in the works). A mysterious virus has killed all the male superheroes except for Superman and Lex Luthor. This leaves the women, which considering their roster, would be more than enough. Despite this, the story really just becomes about Superman and Luthor as they compete in a different set of circumstances. It's another interesting idea not developed enough to make sense.
3 All-Star Batman And Robin
All-Star Batman and Robin drove outside of continuity straight into Crazy Town. This early 2000s alternate take on the Caped Crusader and Boy Wonder should have been a slam dunk, considering it came from Jim Lee and Frank Miller. Instead, it ended up making no sense whatsoever.
About as bad as "I AM A MAN!" is "I'm the God damned Batman." Batman's non-sensical behavior towards a young and traumatized Robin is just one of many things about the story that doesn't work.
2 Brotherhood Of The Bat
It's sort of natural these days that there are many versions of Batman (many more are coming to the big screen in the near future). Once, that wasn't the case and it wasn't necessarily a great idea. In The Brotherhood of the Bat, (also by Doug Moench) a virus has wiped out the world in an apocalyptic future. Right off, one thing that doesn't make sense is the hard lean on tropes that were tired years ago. Another is that Ra's al Ghul decides to clothe the League of Assassins in Batman costumes (plus they all kind of look like him, which is... odd).
1 Speeding Bullets
Speeding Bullets takes an interesting idea and crashes it hard. Instead of being raised by the Kents, Kal-El is raised by the Waynes. He eventually becomes Batman after their deaths. Where it goes wrong is the conflation of the rest of his world. Lex Luthor and the Joker (and the Penguin!) fuse into a misguided pastiche that makes no sense whatsoever. Batman with powers isn't really that interesting anyway, and the story never takes advantage of the potential of the premise.