Even to fantasy there must be some limit Warning: really serious spoilers.
Curiosity led me to tape this off TV, and watch it. I have no fault to find with the acting: Uma Thurman and Lucy Liu, in particular, are excellent, and it is for that, and the undeniably impressive action scenes, that I give a mark of 7. But ...
I am not enough of a film buff to recognise all references, influences, etc., but for me the strongest influence is the comic book, and especially what I have seen from my son's collection of anime. This, of course, is fitting, since much of the action of Part 1 takes place in Japan. But it is most like the comic book in its focus on the central characters, who often seem to be moving in a world where the outside world barely exists and certainly does not interfere with their actions to any notable extent (no police pursuit of The Bride after the killing we see first, for instance; no attempts to find her when she's left the hospital). The central character, The Bride, is effectively a superhero; she survives what ought to be mortal wounds (even a shot in the head!); manages to dispose of two men and get herself into a wheelchair, and from that into a car, when just recovered from a bedridden coma lasting 4 years, apparently; fights and disposes of multiple opponents with only a samurai sword, displaying more than Xena-like agility and stamina and taking only minor damage until her climactic duel with Lucy Liu's character. How the child she was carrying is supposed to have survived is not at all clear(cut out of her after she was shot?); but we only learn this at the very end, in a pretty outrageous piece of manipulation. Maybe it is explained in Part 2(not seen yet).
This presentation of a character without any explanation of her abilities is not confined to The Bride. Lucy Liu's character becomes an expert assassin - fine; but she then becomes the 'boss of bosses' of all the yakuza in Tokyo. We are not given any hint of how she achieves this amazing feat, simply that she has. By this time, she has acquired an entourage of extremely lethal henchmen (and an equally lethal schoolgirl bodyguard), but The Bride disposes of them all (none of them takes a shot at her, even with a bow - they only use swords and other weapons of similar vintage), while their boss waits to fight the final duel, again with a sword only. Why? There is a good deal of extremely gory slicing off of hands, feet, limbs etc., but all those affected survive - they don't bleed to death, as they surely would without prompt application of tourniquets - especially the lawyer whose arm is cut off at the shoulder. But she must survive, to have information that The Bride wants tortured out of her.
Such total disregard for reality grates after a while. Comparisons with LOTR are inappropriate: in that characters cannot overcome great odds absolutely single-handed, they die (or appear to, in Gandalf's case), take wounds, feel fatigue etc. They still achieve their quest, very much against the odds (but they do have some magical help at crucial moments), but they seem much more plausibly human.
Ultimately, this film is a series of spectacles, which one is meant to admire without questioning any details of their presentation. I cannot suspend disbelief to that extent; but I will watch Part 2 just to find out how the end happens (I know from reviews the barest outline of what happens in it).