The art by Jason Fabok is immaculate. The way he drew the different Jokers, they all look similar but at the same time, with their own unique characteristics, that readers can tell them apart, and that's due to the meticulous details on Fabok's art. Simply amazing.
As for the story, it was ingeniuous how Geoff Johns explained the only lingering nitpick I had with the Killing Joke. Do not get me wrong, The Killing Joke is easily one of my all-time favorite comic book stories of all time, along with The Dark Knight Returns, Batman Year One and Batman The Man Who Laughs. However, that bit about how the Joker's wife was killed due to a freak accident involving a baby bottle just didn't ring true. No one can die from heating a baby bottle. That made no sense. But I didn't let it bother me, and just used a little known thing among comic book readers, "suspension of disbelief". Yes, that bit made no sense, but it didn't hinder me in my enjoyment of the Killing Joke.
As for the nit picks by some people in message boards and comments sections...most of them are just born out of misunderstanding the story. For example, the most egregious complaint people have over the Three Jokers is that "duuuhhhh, if Batman knew about the identity of the Joker, why did he ask the Mobius Chair?" Hahahaha! That is hilarious. Batman also asked the Mobius chair the identity of the murderer of his parents, a question he already knew the answer to. Batman was simply testing the chair, and not at all a plot hole.
About the question on whether this is part of continuity...well, yes, of course it is. How can it not be? It directly referenced the Killing Joke, A Death in the Family, Under the Red Hood and other stories clearly within continuity. Barbara Gordon was the Oracle for years in the DC Universe because of what happened to her during the Killing Joke, and The Three Jokers clearly takes cues from the Alan Moore and Briand Bolland classic.
As for whether the "Comedian" is the original Joker or not, I believe so. The Three Jokers essentially established that the Killing Joke is the one true definitive origin of the Joker. And, really, as far as origin story goes, you can't really go wrong with the Killing Joke. That is a modern day classic.
As for the question on how many times did Batman fight against the other Jokers? Well, it's not really important. When those stories were written, the writers intended for the character to be the original Joker. The Three Jokers is just a way to streamline the incongruous portrayals of the Joker through the years. At least, with this, DC did not do away years of continuity, the way Marvel did it when they undid the marriage of Peter Parker and Mary Jane Watson with that awful One More Day nonsense. Every fight between Batman and Joker happened, they may not all be the original Joker, but Batman was in fact fighting versions of the Joker at those times. Now, we are left with one. This last Joker standing even knows that Batman is Bruce Wayne, which is compatible with how the Joker knows Bruce Wayne is Batman in the Joker War.
This mini series may not add much in the Batman mythos and there was no earth-shattering revelation, but, not all stories need to have a major twist in order to justify its existence. Sometimes, a tale only needs to tell the stories of its characters and that is good enough.