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.
Fans are split between whether this a story that intelligently analyzes Batman, the Joker, and the relationships the two have with each other as well as their cohorts under a very dark and amazing lens, or a retreading of the same storylines and themes that almost all encounters between the two deal with nowadays while turning Joker into a Villain Sue.
Similarly, Joker losing his face (and some of the gory acts he commits in the storyline) is either creepy and edgy in terms of character demonstration, or ridiculously over the top and impossible to take seriously. Interestingly, Detective Comics #1, where Joker gets his face removed, was written by Tony Daniel, but before his plans with that idea were revealed, he left Batman, and the Death of the Family saga's writer, Scott Snyder, had to deal with the removed face and go in his own direction with it, since it would be very difficult to effectively retcon.
Complete Monster: The Joker once again establishes his position as one, particularly with his treatment of Harley Quinn in the story.
This is essentially confirmed by some of the interviews with Snyder detailing his ideas for a follow-up when the Joker inevitably comes back; Plus, when Batman declares that he's through with the dances and games and the like in the finale, the Joker appears to be slicking back his hair and adjusting his tie in a manner that suggests he expects Batman to confess his love for him at last.
Ho Yay: The Tim/Jason relationship, including the way the Joker positions their bodies after knocking them out, gives off this vibe.
Jerkass Woobie: Harley Quinn. It's no secret that she is a villain. However, when you see the Domestic Abuse Joker puts her through and the fact that she's not really enjoying it this time around, you will feel sorry for her.
She goes so far as to tell Batman how whacked out the Joker is this time. Now that's jarring for her character.
Magnificent Bastard: The Joker using incredibly meticulous planning and master manipulation in order to break up the Bat-Family. And it works.
Narm: In Batman #16 Joker at one point dramatically in a one page spread yells for Batman to "Sit. [His] Ass. Down!" Only for the word "ass" to be censored, in a series that involves the Joker wearing his decomposing face as a mask, as well as beating a child on-panel.
Lots of the Joker's lines come across as this.
Joker wearing his own face as a mask can come off as really dumb and trying way too hard to be freaky.
Nausea Fuel: The Joker's face has begun to rot in the year since its removal.
Squick: Joker got his face back, and he's used a belt to wear it like a grotesque mask. He wears it upside at one point, with his eyes visible from it's mouth and vice versa. Towards the end of the story it even begins to rot.
They Wasted a Perfectly Good Plot: The aftermath of the story was swiftly forgotten about less than two months later, with the fallout of Damian Wayne's death in the unrelated Batman Inc. #8 taking precedence in the Batman books. Nightwing and Red Hood & the Outlaws were the only two titles directly affected, with Nightwing relocating to Chicago after his Trauma Conga Line and Red Hood choosing to have his memories erased because of how much the Joker has affected his life, whilst Teen Titans and Batgirl carried on as if nothing had happened.
A criticism of the time was that the reason the event couldn't work in the first place is because, as of the New 52, there was no real family to 'kill' and Batman had turned from being an Informed Loner into an actual loner.
Villain Sue: The Joker has been criticised by many for being this. Some complaints say he borders on Jeph Loeb's Hush levels at times.