Factual error: In the scene when Zhen is writing down the characters of Shu Lian's name, she writes the modern form of the "Lian". That form wasn't introduced into the language until after World War II, and this movie is set well before the fall of Imperial China.
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.