Batman is now known as a superhero who refuses to use a gun or to kill (well, most of the time). This was not true in the first year or so, although he didn't actually kill humans very often and most villains died from Karmic Death. See Pay Evil unto Evil. Another notable case concerns events in the story arc Hush. The titular villain appears revealed as long dead Robin Jason Todd, before he turns out to be an imposter (and not the real Hush, at that). Later, a retcon revises the story so that it was a resurrected Todd after all, but he escaped to be replaced by the imposter mid-battle.
Since while everyone's histories were changed for the New 52, Batman's was largely unchanged — meaning while superheroes only appeared 5 years prior to its events, Batman had to be in action for ten because he still had four Robins in his history.
One constantly-wavering element (possibly the only one, since Batman's overall setting is more amenable to Like Reality, Unless Noted than most of his fellow heroes') of Batman's backstory is the nature of the man who killed his parents. Originally a nameless mugger that Bruce never saw again, later retcons in the '40s and '50s gave him a name (Joe Chill) and a new history as a professional hitman deliberately sent after the elder Waynes by a local mob boss. Since then, almost every big reboot has changed up whether he reentered Batman's life (Mike W. Barr's Batman: Year Two was perhaps most audacious in this regard, actually having Batman team up with Chill) and what kind of Karmic Death - if any - he suffers for creating crime's greatest nemesis.
Despite the fact that Cassandra Cain's entire upbringing was a never ending training from hell, she did love her father, and yet she ran away from him. The reason was that her first kill was the very first time she had witnessed death up close and due to her body reading abilities she thought it to be very, very, scary. Thus she found out her upbringing was evil. Now enter the last issue of Adam Beechen's mini series about her where it is revealed that she hated her dad all along, and that she had actually witnessed her father committing murder up close many times before her first kill.
Birds of Prey: In the Blackhawk comic series, when Zinda Blake was brainwashed by Killer Shark to be his partner Queen Killer Shark, she had no loyalty to him. She abandoned Killer Shark to escape the Blackhawks twice in Blackhawks #200 and #204. And when Killer Shark and Queen Killer Shark capture the Blackhawks in #225, she betrays him, threatens his henchman to turn on him, and imprisons him with the Blackhawks. In Birds of Prey, her brainwashed personally is shown to be completely loyal to Killer Shark, with her being completely in love and devoted to him, to the point that it's implied that she has been sleeping with him in the past.
Stephanie Brown died at the end of Batman: War Games, as after she was tortured by Black Mask, Leslie Thompkins withheld vital medical treatment. Her autopsy photos were shown to prove the dangers of crime-fighting to Misfit. Later it was revealed she never died: Leslie faked everything because her secret identity was compromised, her body was switched with an overdose victim with a similar body type, and Batman knew this all along making his relationship with Tim Drake even more strained since he neglected to clue him in.
The stories began contradicting themselves after only one year. Teen Titans had Tim Drake mention his time as Robin and that there had been prior versions of the Titans. When the trade paperback came out, this was revised with Tim always being Red Robin (never regular Robin, though still Batman's sidekick), and omitting mentions of prior Titans.
The Titans were also originally referenced in the Batwoman series, with Flamebird claiming to have been part of the team and having fought Deathstroke. This dialogue also found itself edited when it came time for the trade paperback to be released.
The thing with Tim never having been a Robin was left in when it came to the trades collecting Batman, with the Bat-Computer specifically mentioning it.
Dick Grayson and Barbara Gordon's relationship was retconned in the 1990s. Pre-Crisis, Batgirl was almost a decade older than Dick and the two had a purely platonic relationship. Since the '90s, however, Barbara (now aged down to be either the same age as Dick, if not slightly younger) is treated as one of Dick's first loves dating back to his days as Robin.
