It's pretty common for Asian movies to suffer from cuts and translation changes when released in the United States. These aren't mistakes in the translation, but deliberate changes made to the message. For instance, in Fist of Legend, when Chen Zhen (Jet Li) is asked by Mitsuko (Nakayama Shinobu) if he hates the Japanese, his response changes depending on which version of the film you're watching:
Original translation: "I don't know."
American release translation: "I don't hate."
The American release of Hero was no exception to this. A number of scenes were trimmed or edited, and the translation was changed more than once. In the original version, the king (Cheng Dao-ming) tells Nameless (Jet Li) that his duel with Broken Sword (Tony Leung) was to honor Flying Snow (Maggie Cheung). In the American release, the king supposes that the duel was fought in their heads and not for real. Here's a more major change, though - in the original Chinese releases, Broken Sword's message to Nameless is "All Under Heaven." In the American release, the translation was changed to "Our Land." (I typically avoid American releases of Asian movies, for this reason, preferring to nab Asian imports. However, I don't mandate that you guys do the same in this course.)
What are the impacts of a domestic studio deliberately changing the translation of a foreign language film?