Revealing mistake: When the swordmaker writes "Bill" on the window, take a close look. The window has been wiped before (as happens at the end of the scene) and "re-steamed" - you can see the outlines of the wiping from earlier takes, with a clear contrast between that pane and the others. (00:52:45)
Revealing mistake: When The Bride is calling out O-Ren, Sofie Fatale has her arm on the building's beam. If you look at her arm, right where The Bride is about to cut, there is a visible seam in the sleeve. (01:11:10)
Revealing mistake: When Gogo is fighting the bride, misses and hits herself with the mace, as she falls backwards onto the table, you can see the stunt double's hairy legs. (01:16:10)
Revealing mistake: When the Bride is fighting the General of the Crazy 88's he slashes at her lower torso and scores a hit, but the slash on the Bride's jacket is already there before he strikes (it is not there in the previous scenes and when he slashes it makes the sound of him cutting the material). (01:23:10)
Revealing mistake: During the restaurant fight scene, Thurman's fight double can be easily spotted from time to time as she is a few inches shorter and a little heavier than the star. It is especially noticable during the silhouette sequece. (01:23:30)
Revealing mistake: When the Bride takes a slash at Buck's heel, you can plainly see that there is a fake heel there. She definitely cuts through the sock, so it's not the sock pattern, and there is no blood.
Answer: Bill used Hattari Hanzo's teachings for evil, instead of belief and self defense.