Possibly many examples, most of which would pertain to the Dark Knights' backstories. For example:
For the Dawnbreaker, did he ever get a chance for romance with Talia or Selina? Or did he just murder them both in cold blood like the rest of his rogue's gallery?.
For the Red Death, just what exactly happened to his Bat Family? Obviously they died but how did it happen and did he seek revenge upon his rebirth?
For the Devastator, how many died during Superman's reign of terror? Bruce said Lois' death was what pushed him over the edge, but who else fell victim before her?
For that matter, we never get a specific answer as to what caused the Devastator's home universe's Superman to be corrupted. However, in the introduction to the Devastator's origin, we see Superman's eyes glow purple, and combining this with the beginning monologue this Bruce has about this Clark's FaceHeel Turn, this seems to be implying that some sort of external force of some kind caused the aforementioned corruption.
Also, at the end of Dark Nights Metal, He gets destroyed along with most of his fellow Dark Knights thanks to Element X. However, since the Devastator has Doomsdayspowers, is it possible that the Devastator will eventually come back and be immune to Element X?
For the Drowned, what happened to her Bat Family? Did she ever even have one?
For the Murder Machine, was it a quick conversion from man to machine? Was it painless?
For the Merciless, the war was stated to last two years before Bruce took the helmet. How many casualties happened during that time? Did Bruce have anything left to lose besides Diana?
For the Batman Who Laughs, when he spoke with the Bat Family regarding his Jokerization, he mentioned confirming his suspicions earlier that night. Did he really mean that his conversion happened just a few hours ago? If so, it only took a few hours, if that, to formulate a plan to bring Barbara, Jason, Dick, and Tim together and slaughter them in cold blood. And considering what he did to the Bat Family: What did he do to Alfred?!And what happened to his eyes that he chose to cover them?!
Also, over the course of his murdering Superman, The Batman Who Laughs seems to mutate ever further as his smile grows bigger and bigger, until by the end it takes up pretty much the entire mouth area of his cowl! And he even leaks blood from the mouth as he speaks to the bandaged victim! What is happening to him?!
By the time it was too late, was Bruce ever even aware of what was happening to him? Did he go to sleep one night and the Batman Who Laughs woke up instead? Did he have a nightmare a la Arkham VR that sealed his fate inside his own mind? Or did he have to watch himself in the mirror as his skin grew paler and paler, his hair turned green and his lips parted in a demented grin?
For The Grim Knight, the mere fact that Bruce seems to have no known companions aside from Alfred. And even then, in the end, Bruce was almost set to kill Alfred simply for leaving. If that was almost Alfred's fate in the Grim Knight's home universe, what happened to the Grim Knight's Bat-Family? And for that matter, since The Grim Knight executes criminals, what happened to Talia and Selina?
If what Barbatos says is true, he's manipulated Bruce Wayne's entire life following his trip through time after Final Crisis. How much of Bruce's life was part of what came naturally and how much of it was part of Barbatos' manipulation?
We only have the Batman Who Laughs word on him picking "the worst" of Batmans Dark Counterparts, but as evidenced by The Red Death being a weak link from not being "fully Bruce Wayne" it's more likely he picked them due to them being JLA counterparts rather than how bad they were, seeing as some of them have truely sympathetic backstories and not being actual evil just, broken by their worlds. There may have been several more worse Batmen, even after the events of metal as the Dark Multiverse still exists, and unlike the Light Multiverse, Nightmare worlds are constantly being made and destroyed every time someone has a fear, for instance one possiblity that may exist is a Batman who accepted Ra's offer and became the Demon Knight.
The worlds in the Dark Multiverse all begin to collapse as soon as any variation of Batman/Bruce Wayne kills the bad guys. Considering Batman's enemies are considered some of the most entertaining villains in comic book history, it's essentially saying that a Batman who kills will inevitably run out of stories to be told.