I don't buy the central idea. It's attention-grabbing and I suppose it succeeded in its goal because I bought this book, but I think having three Jokers dilutes him. (I also don't believe that they'd all work together without killing each other. Without getting into spoilers, something towards the end here was pretty much guaranteed by putting multiple Jokers in the same room.)
Geoff Johns's idea is that the Joker's been written in so many different ways over the years that he might as well have been different people. (Surely that's even more true of Batman himself?) This book's three Jokers are:
1. The Criminal, who coincidentally looks a bit like Mark Hamill (his best-known voice actor). He's meant to be the Golden Age Joker, from the character's earlier, more serious appearances. He claims that laughing hurts him.
2. The Clown, from silly Silver and Bronze Age comics. He has his original sidekick Gaggy (introduced in 1966), he makes Jokerised fish (including a shark!) and he talks about beating Jason Todd to death in "Batman: A Death in the Family".
3. The Comedian, who's been taken so directly from Alan Moore's The Killing Joke that this book's practically a sequel to it. (This even uses the 3x3 grid that reminds me of Alan Moore, c.f. also Watchmen.) This Joker talks about shooting Barbara Gordon in that story and there are huge references to Moore's version of the character's origin as a failed comedian.
(No Harley Quinn, though. Odd.)
Helping Batman against these three are, appropriately, Jason Todd (Red Hood) and Barbara Gordon (Batgirl). I don't mind Barbara. I have massive objections to Jason, though, since I find him more of a hate figure than the mass-murdering Jokers. He's a cock. Finding him in a story is like finding piss in your breakfast cereal. This is a character whose idea of looking for information is to beat up toxin victims. He changes his mind from page to page on whether or not he wants to kill the Joker. He swears to kill him. Then he swears not to kill him. Then he swears to kill him again. Sigh. Couldn't he have sworn instead to embrace rational thought? The book's happiest moment is the sight of Jason getting beaten nearly to death for old time's sake (among other reasons), although disappointingly this doesn't reach its ideal conclusion.
In fairness, though, Jason's calmed down by the end of the story and plans to attempt self-examination, having undergone a character journey that semi-pseudo-justifies his presence in this book. (I'd have enjoyed this story more had the Jokers' plan for him succeeded, but Frank Miller's already done that one.)
Barbara is fine. Batman's kind of boring, which can't just be because everyone else is more colourful because that's normal for him. In fairness, though, he gets his share of meaty emotional material.
I like the story being told. It has meaningful character journeys, discoveries and revelations. (I like the one at the end.) If you're going to tell a multi-Joker story, it makes sense to do this. They're trying to make a better Joker, although ultimately their most serious attempt at this is a lot like (again) The Killing Joke and no likelier to succeed than that was.
I like the Joker toxin hordes, though. And the shark is cool.
Overall, I quite like this book... but part of that is the fact that it's a non-canonical Black Label release. I don't like the three Jokers idea, but it was worth doing once, as an experiment, and I think the results worked quite well. This book has strong emotional beats and a point. Its characters have journeys and a reason to be in the story. I like the art. The book's only problem is Jason Todd, to be honest.