I wasn't sure. But I thought surely there was some relevance to the colour changes beyond simply the frame of reference (i.e. Nameless - red, Emperor - blue, "reality" - white).
There's an incredible review of the film at the film review site I trust most:
http://www.filmfreakcentral.net. The reviewer, Walter Chaw, is the only reviewer I find myself agreeing with 90% of the time, and he's a damned good writer.
Edit: Here's the specific link, and an excerpt:
http://www.filmfreakcentral.net/screenreviews/hero.htmThe sexual heat between assassin Broken Sword (Tony Leung Chiu Wai), his lover Flying Snow (whose name, in Chinese, is a homonym for "Flying Blood" (Maggie Cheung)), and Broken Sword's calligraphy student, Moon (Zhang Ziyi), presents Hero with its central conflict. Those human attributes of sexual jealousy, pride, legacy are all placed in the crucible of something immeasurably humble. The most improbable product of the hugeness of this epic is the modesty embodied in its resolution. Zen isn't a personal thing, it's the ambition to be utterly indistinguishable from everything: a slaying of ego, a quiet absorption into the universe. And Hero is likewise about the laying down of the petty conflicts and revolutions of man in favour of a larger, holistic whole. It's a peace constructed from more than a lack of war.
The fight sequences are extraordinary in their poetry--this may be the most beautiful film ever made in the digital age--and matched by a spirituality that finds secrets and whispers in the way a man writes a word. Hero suggests interconnectedness, between all things and all actions, so that every gesture carries the weight of cathedral bells. It's chaos theory reduced to its formalist logic, and Zhang does the impossible by balancing the majesty of a martial arts extravaganza with the chamber opera of interpersonal drama. This is the best mainstream film to come out of mainland China since Hong Kong returned to the bosom of the motherland, because it finds that patiently unravelling thread of hope in the heart of the Chinese that their time beneath the yoke of oppression will end one day. And it'll end as a result of small people like themselves finding the courage to lay aside their small dreams to, at some critical moment of transcendence and metastasis, change the world.