My conclusion is that Kill Bill is a movie that really depends on you having the proper context to fit it into. If you do, it all makes perfect (beautiful even) sense. If you don't, it's going to seem like a pointlessly bloody piece of overwrought mayhem, and you'll probably want your wasted 111 minutes of life back.
Kill Bill is the best filmed manga I've seen. If you look at it as a live-action version of the traditional revenge story-line type of Japanese comics, everything falls into place. Including the great gouts of arterial blood, entire sheeting rains of blood raining down on various people (in a fashion which, anatomically speaking, is quite unusual for some of the causal wounds) - it's true that much blood doesn't make sense from a natural or filmic standpoint, but think about the drawn versions of similar scenes. That 'spray the room with blood when the sword is withdrawn from the body' effect is a standard paper-comic trope. If you translate the scene from 3D to 2D mentally you can see the similarity.
The kicker (or obvious signpost, if you will) is the animated vignette about O-Ren Ishii's childhood. But other indications are there in the chapter titles, the Bride's very formalized speech to Vernita Green's child, and the entire interaction between the Bride and Hattori Hanzo (but especially the presentation scene).
There are lots of other references, overt and subtle, to everything from Hong Kong action flicks to anime to Lone Wolf and Cub... Most of the laudatory reviews I've read link the lineage to Bruce Lee & Sonny Chiba films, so I was expecting a lot more visual riffing in that direction - and Sonny Chiba himself has an excellent turn as the elder statesman (whose aid must be enlisted in part because he was present at the root of the problem). But I'm going to stick with my 'filmed drawings' interpretation - because of the pacing, because of the dialog, and because I can so easily abstract each of the scenes into black-and-white manga-style pages in my head. Speaking of b&w, let me add the whole Crazy 88's fight sequence as evidence, too.
On a separate-but-related note, I really got a kick out of the names. From the Deadly Viper Assassination Squad (complete with cheezy code names: Cottonmouth! Black Mamba!) to Sofie Fatale and GoGo Yubari, and of course the Crazy 88's. I didn't get an exact count, but Uma's Bride may well have chewed through eighty-eight of them to get to O-ren...
So that's my take on it. I'm looking forward to Vol. 2 - I'm curious to see where Tarantino goes with this.