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.
"I would rather be a ghost, drifting by your side...as a condemned soul...than enter heaven without you. Because of your love...I will never be a lonely spirit."
The scene where it was just Mu Bai and Shu Lien sitting together and Mu Bai taking her hand and pressing it gently to his face. That small, simple gesture spoke volumes about how he felt for her and the look on her face said the exact same thing.
Lo and Jen's relationship.
Also, the brief scene of the two minor characters, the servant Bo and the police inspector's daughter May, after Jade Fox had killed her father. Bo was standing on guard at her house in case Jade Fox returned. May came out and quietly told him to come inside because since both of them are scared, at least they could be scared together.
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.
Unfortunate Implications: Women probably shouldn't rebel and resist being shoehorned into pre-ordanied roles in society, as it will ruin their lives.
Partially justified; this film is coming from a society that places much more emphasis on order and harmony than they do on justice and human rights. That also partially explains the seemingly pro-dictator message of Hero. Us Western audiences, if we wanted to minimize some of the values dissonance, could excuse Jen's unsympathetic portrayal in the film by focusing on the damage she causes in her attempt to be free. Pixar recently did something like that with Brave, too.
Part of the reason it resonates with Western audiences is because it also counts as a case of Be Careful What You Wish For; Jen ends up free to live with her rebel lover, at the cost of her family and Mu Bai's mentorship. Breaking free of the system got her what she thought she wanted, but if she'd stayed and looked for loopholes in the society she lived in, she could have kept her family, who would have been proud to have a Wudan warrior as a daughter - who they obviously couldn't marry off as a bargaining chip, as the only kind of man who'd be willing to live with a Wudan warrior would have been, well, a rebel.