Other mistake: It is stated by the caption ("The far East; 3 years later") that the events of most of the movie take place 3 years after the prologue. Thus, both Nicolas Cage and Hayden Christensen have made it to China and learned flawless Chinese (there's no language barrier whatsoever and they understand each other perfectly at all times) in less time than that, while being on crack and on other considerable hardships, too.
Other mistake: Prince Shing and the King have a conversation that lasts not less than 5 minutes of movie (which compresses the time somewhat; groups of people get in and out of the large hall, which wouldn't be instantaneous and happens at least 3 times). The conversation happens while the other members of the royal family are running away through a secret passage. With such a considerable head start and wasting no time (they keep moving even when they put mantles on), they are reached by heavily-armored guards, through the same secret passage, within seconds. (00:12:10 - 00:17:10)