Continuity mistake: When the army attacks the calligraphy school, the school leader continues writing at his desk as the wall behind him becomes riddled with arrows. After Snow and Nameless go out to deflect the arrows, the camera cuts back to the school leader, and there are far fewer arrows in the wall behind him than there were before. (00:23:10 - 00:25:40)
Continuity mistake: When Nameless defeats Moon the first time in their duel as Broken Sword and Flying Snow fight, he holds his sword horizontally against her throat. In the next shot it's vertical. (01:03:50)
Continuity mistake: During the scene where the calligraphy students continue their work and the arrows are continuing to shower through the classroom, there is a wide shot of the classroom and a number of arrows are hitting the students and landing near them. Shortly after this there is a shot taken from the same angle but a number of differences. The position of a number of arrows have changed (with some disappearing) but you can also see an arrow in one of the students backs has disappeared. Another arrow has landed in a bowl that was knocked over before and is now standing upright. One of the dead students the arrow in her head has disappeared and her head has moved between shots. (00:22:10 - 00:24:30)
Answer: Those were two different swords they had at the end. You can tell because when Broken Sword's weapon hits the sand when he drops it, you can clearly see the tapered point, not a broken edge.