Revealing mistake: Just after Li Mu Bai tells Shu Lien that they are very close to her headquarters and that she should check in, we are treated to two 'time pass' shots of forest. The second of these features some very obvious power or telephone lines in the lower right corner of the screen.
Factual error: When Jade Fox fights the policeman and his daughter, immediately after the fight starts you see birds taking off from trees with the full moon in the background barely above treetop level. The note leading them there said to meet her at midnight. They said she was "unpunctual" but for the full moon to be barely above treetop level she would have to be nearly six hours late. A full moon is straight up at midnight.