These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Base Breaker: 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.
Crazy Awesome: 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-Might, 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.
Ensemble Darkhorse: 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.
Fridge Horror: In Final Crisis, Batman was kidnapped by Darkseid's minions and had his DNA and memories harvested to produce a clone army. The clones went insane from the decades of emotional trauma the original had to go through and killed themselves. In the final issue of Batman Incorporated, Ra's Al Ghul is revealed to have an army of cloned Damians. Considering that Damian has all the combat training his father has minus the years of tragedy that prevented Darkseid from having his army of Batmen, this means that Ra's Al Ghul has effectively learned from Darkseid's mistake. So much for Final Crisis.
Jerkass Woobie: 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.
Jerk Sue: Much debate exists within the Bat-Fandom over whether Damian Wayne is a Deconstruction of one of these or one played very straight. He tends to get away with pulling a lot of shit that few others would get away with, but at the same time it's made very clear that no one really likes him that much.
Again, debate rages over how true this is, but it is undeniable that Damian Wayne, at his first appearance, was the Scrappy and was even called Cousin Oliver in Red Robin 14.
Batman/Bruce Wayne himself has been accused of this during Morrison's run.
Moral Event Horizon: Talia al Ghul orchestrating the brutal murder of her own 10 year old son, although lately is 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 decapited her other son, The Heretic, in Batman Incorporated v2 # 12.
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: Morrison's run is notably the onlynote Whilst the Green Lantern books under Geoff Johns remain intact, they did undergo a major shake-up in the status quo at the time of the reboot thing to enter the New52 unscathed, with Batman Inc. Volume 2 carrying on his pre-reboot story completely independant of the other Bat Family titles. If the reader didn't know about the reboot, it would simply appear that everyone just decided to spontaneously change their costumes.
Stoic Woobie: This trait of Batman is even more pronounced here than in the main books.
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.
They Changed It, Now It Sucks: Jason Todd's fanbase weren't happy with what Morrison had done with him, both in looks (HOW DARE THEY MAKE HIM UGLY!!) and costume. And this is after his appearance in Battle for the Cowl, the damage was so great they had to get the man who had originally brought Jason Back from the Dead to fix it. Fans were even upset about Jason's hair. In most post-Crisis continuity, Jason's hair is jet-black, but in pre-Crisis continuity, it was strawberry-blonde. Morrison tried to reconcile the two colors by stating that Jason was forced by Batman to dye his hair black to make him look more like Dick, which in turn makes Batman look like a jerk. However, there are a few problems with this. The first is the fact that the color is wrong. In Batman and Robin, Jason is depicted with crimson-red hair, despite having been given strawberry-blonde hair in pre-Crisisnote Compare a bright red to a pastel orange. The second is that in pre-Crisis continuity, Jason died his hair of his own volition in order to make himself look more like Dick. Batman had no say in it. And third is that Jason had been depicted with jet-black hair in situations where it would be implausible to have his hair dyed, such as the years he lived as an amnesiac vagrant in between escaping his grave and being taken in by Talia.
Morrison seems to have retconned or ignored what he did to Jason as of Batman Inc (v2) #4
Uncanny Valley: The Heretic is absolutely steeped in this once his helmet comes off. A baby's head on a giant man's body? That's some nightmares right there.