Base-Breaking Character: Damian Wayne. He has a loyal fandom, but also a very vocal hatedom. His death shattered his fandom into people who thought it was handled well and people who thought it was simply not okay.
Broken Base: Batman driving Joe Chill to suicide and doing nothing to stop it. Fans either like it or hate it for making Batman indirectly murder a big part of his motivation.
Character Rerailment: After several notoriously awful attempts to shoehorn Red Hood into the DCU (such as Countdown to Final Crisis and the Nightwing "One Year Later" storyline), Morrison's run on Batman and Robin returned him back to relevancy as a psychotic villain and a dark reflection of Batman. However, it didn't last, as the New 52 reverted him back to an angsty teenage rebel, albeit one who's actually on fairly good terms with the Bat-Family, if not somewhat estranged.
A dark reimagining of classic sidekicks. Damian Wayne is a deconstruction of hyper competent sidekicks, Bucky Barnes was made Darker and Edgier to fit the WWII stories.
Update older material for modern times. Lots of Batman's Silver Age material was said to be hallucinations or outright made canon, while Cap had brought back the Cold War-era Captain America and had him a true Man Out of Time, racism included, and the previous Bucky.
Their first sidekick taking up their mantle. Dick Grayson, the original Robin, became the next Batman while Bucky Barnes, the first Bucky, became the next Captain America.
Said former sidekick learning to be Batman/Captain America "their own way". Dick learns to embrace his happier ways and treat his Batman as a performance, whereas Bucky learns to embrace his darker tendencies like using guns.
The successor fighting someone attempting to imitate their dead predecessor in dark ways. Dick fought a returned Jason Todd, once again trying to be a brutal vigilante cleaning up Gotham with murder, while Bucky fought the crazy Cold War-era Captain America who was working with White Supremacists.
The "dead" character travelling through time instead of dying. The Omega Sanction sent Bruce back to the Stone Age and he made jumps through time to the present, while Red Skull's bullet trapped Steve in a loop of events that he couldn't prevent, lest he damage the time stream.
The return of the main character who then loans their successor their title while taking up a higher position of power. Bruce returns and lets Dick stay Batman and forms Batman Incorporated, while Steve returns and lets Bucky stay Cap while he heads up SHIELD.
Lord Death Man, archenemy of Mr. Unknown, is a psychotic Badass in a Nice Suit who wears a skull as a mask, runs around with a freaking tommy gun, can somehow come back from the dead no matter how many times he's killed, and at one point tries to kill Jiro's girlfriend with a giant squid that he shoved into a small apartment. Grant Morrison notes in the deluxe edition that the guy is basically a Grand Theft Auto player character made as a supervillain.
The Batman of Zur-En-Arrh. Literally, as he's become quite insane at this point. Dresses in a bright red, yellow, and purple costume meant to display how he's even more confident, kicks all kinds of ass with nothing but a baseball bat and some garbage he uses for batarangs (a tin can lid and a wreath are seen in one page) and spouts such lines as "I am the Batman of ZUR-EN-ARRH!" (Uh-oh.) and "You can't fool the Bat-Radia, it sees through your lies!" To top it off, he's followed around by Bat-Mite who may or may not be a figment of his imagination, and converses with gargoyles while planning his attack.
Most of Batman Inc. could be considered Crazy Awesome in their own right, but special mention goes to El Gaucho, Dark Ranger, and of course Bat Cow.
Crosses the Line Twice: The Joker's first appearance in the series, shouting "I did it! I finally killed Batman! In front of a bunch of vulnerable, disabled kids! Now get me Santa Claus!" Followed by Batman throwing a badly wounded Joker into a dumpster.
Beryl Hutchinson. Originally, Beryl was introduced as a one-shot character during Morrison's run on JLA, then she had a prominent role in Morrison's JLA Classified arc where her competency helped save the world.
Amongst the members of Batman Inc., Nightrunner seems to be really popular amongst fans despite his small role.
Epileptic Trees: Naturally from a Grant Morrison work, most of which revolved around the Black Glove's identity. Fans' attempts to make sense of everything were also lampshaded/poked fun at by the Joker.
Fan Nickname: DickGrayson as Batman is either referred to as Bat-Dick or DickBats to differentiate him from Bruce, THE Batman.
Morrison makes Damian this over the course of his run: Cocky reckless brat, really messed up family, and a maximum of two people who actually like him. The conclusion of Batman Vs. Robin alone is enough to make you want to hug him. And then there's what he's going through in Batman Incorporated: being told to go back with his mother or else she'll do something horrible. This is the woman who threw him aside when he disagreed on what path to take and he has to leave the family he's maybe starting to fit with. To make it worse, the storyline brings up his possible Bad Future of Batman #666.
Red Hood. Yeah he's a dick who wants to enforce the law in Gotham through brutality, but he gets put through some seriously undeserved shit when Flamingo comes to town.
Moral Event Horizon: Talia al Ghul orchestrating the brutal murder of her own 10 year old son, although it is later revealed that she didn't order Damian's death. It was the impulse of her large, unstable Damian clone and her Leviathan goons. She eventually crosses the MEH when she decapitates her other son, The Heretic, in Batman Incorporated v2 # 12.
And that's ignoring the fact that, in this continuity, she date-raped Batman to make Damian in the first place.
Flamingo EATING FACES WHILE HIS VICTIMS ARE ALIVE.
The Heretic's face: the head of a baby in a body of an adult.
(Un)Surprisingly, Batman himself in one chapter. After locating Joe Chill, the man who killed his parents, Batman stalks him for several nights. Then Batman, the man who swore never to commit murder, drove Chill to suicide! No wonder so many Batman villains are nuts. Sane people don't last long enough.
Protection from Editors: While Morrison's run survived the New 52 reboot relatively intact, it did suffer from several changes, such as the absence of Oracle, Cassandra Cain, and Stephanie Brown, as well as a number of costume changes to make the series part of the New 52 continuity.
Rescued from the Scrappy Heap: Damian, throughout the course of Batman and Robin, mellows out and shows not only his softer side, but also his loyalty to Dick.
Stoic Woobie: This trait of Batman is even more pronounced here than in the main books.
Jason Todd's no holds bar smackdown on Damian Wayne in Batman and Robin #6, which ended with Damian getting a broken back for his trouble.
Arguably it's Jason who receives the beating here at the hands of the Flamingo, a killer in a bright pink costume that would have killed Jason and his sidekick Scarlet if Damian and Dick had not come to his rescue. It was also Flamingo who shot Damian in the back, paralyzing him.