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.
Answer: It is an open question. Interpretation of the last scene is really left to the audience. But to those of you who completely missed the whole point of the jump, it refers to the "Legend of the Mountain" as told to Jen by Lo "Dark Cloud". He told her that if a person makes a wish and jumps from the mountain, the wish will be granted and, occasionally, the jumper's life will be spared. "Crouching Tiger, Hidden Dragon" is actually a fourth book in the series of five books. In the book, Jen survives the fall, but never returns to Lo, fearing her parents shame and prosecution. Popular opinion seems to be that Jen was in fact in love with Li Mu Bai and the jump was an attempt of escaping the live lover towards the dead one.