These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
It's Popular, Now It Sucks: Go on the Internet and you will find many wuxia fans who don't consider this a "real" wuxia movie, and say that it only became popular because it was made specifically for American audiences and not the more wuxia-friendly China.
Straw Feminist: Jade Fox. She basically comes off as a low-level misandrist after Li Mu Bai's teacher refused to actually teach her, since apparently women can't train at Wudan. It seems, however, that Shu Lien is at least somewhat Wudan experienced as well, as she is the only character other than Mu Bai that can defeat Jen. She can also do the gravity-defying Wire Fu that only people that learned at/stole technique books from Wudan can do. More concretely, Mu Bai says that for Jen, they would surely make an exception, and he (literally) fights to get her to be his student. Maybe Mu Bai's teacher saw that Jade Fox was less than scrupulous, rather than just passing her over due to sex. Seems like sour grapes on her part. Or maybe that's really why she wanted to kill Jen, instead of the fact that she hid her skill and kept Fox from improving.