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. (01:22:40)
Continuity mistake: In the final scene in the cave, the protagonist walks under the rain and becomes wet. After the whole poisonous needle thing, the camera cuts back to her and she is completely dry. (01:41:15)
Continuity mistake: In the scene in the cave where Jen's hands are tied the loose ends of the knot change from shot to shot. (01:01:20)
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.
Audio problem: When Jen is kicking the crap out of everyone in the restaurant, she is supposedly saying a whole load of stuff, but if you watch carefully, she isn't saying most of it, it must have been dubbed. (01:20:30)
Continuity mistake: In the scene where the Policeman, his daughter and a guard fight Jade Fox the policeman throws a disc. Jade Fox spins around in mid-air to avoid the disc, here you clearly see the disc fall to the floor, but in the next shot Jade Fox is holding the disc again. (00:36:20)
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.