Contrary to what some may think, the English-language dialogue in the American version is not a direct translation from Japanese to English. One only has to turn on Literal Japanese-to-English translation subtitles on the region-1 DVD to see that dialogue was paraphrased into comfortable American English.
Japanese mythology tells that dogs/wolves are always male-voiced, and cats are always female-voiced, regardless of sex. For this reason, a man, Akihiro Miwa provides the voice of Moro the mother wolf. His casting is perhaps an in-joke to his career as a female impersonator.
Mononoke means angry or vengeful spirit. Hime is the Japanese honorific word that means princess, which, in the rules of Japanese grammar, is placed after a person's name instead of before, as is the custom in many Western languages. When the film's title was translated into English, it was decided that Mononoke would be left as a name rather than translated literally.
When it was announced that the Miramax/Buena Vista region-1 DVD would only contain the English-language dialogue track adapted by Neil Gaiman, there was enough fan protest to convince Miramax to delay the release in order to include the original Japanese-language dialogue.
Neil Gaiman, in Anglicizing the script, chose to simplify some plot elements to provide a cultural context for phrases and actions not well known outside of Japan. Specific terms like Jibashiri and Shishigami, for example, are changed to the more general Mercenary and Forest Spirit. On the English language DVD, the subtitle options have a literal translation of Hayao Miyazaki's script in addition to Gaiman's adaptation.
Disney/Miramax, which released the film in North America, was contractually obligated not to edit any footage out for its North American release. They asked to, but were refused. Although they kept their end of the bargain in not editing the film, they did release it into far fewer theaters than promised and expressed surprise that it had made little money at the box office.
While Princess Mononoke (1997) was acquired after it was released in Japan, its American release was delayed for almost two years, allegedly because of a negative reception at a St. Paul, Minnesota test screening.
The trivia item below may give away important plot points.
When Ashitaka intervenes in the fight between Lady Eboshi and San, Eboshi exclaims that she's tired of Ashitaka's cursed right armed, before shouting "let me just cut the damned thing OFF!" Later in the film Eboshi loses her right arm to Moro.