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)
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: While fending off the arrows in front of the calligraphy school, Nameless jumps outside and kicks shut the door. He jumps to the upper level and we see the doors behind him here are also closed, except for one shot when they are open. (00:26:10)
Continuity mistake: When Nameless goes to see Broken Sword's finished calligraphy after the archers attack, a strand of hair is over Broken Sword's face in the closeups but not in the wider shots. (00:27:35)
Continuity mistake: After Flying Snow stabs Moon in their fight, shots on Moon show her consistently bent over but shots on Flying Snow with Moon in the background sometimes show her standing up. (00:38:30)
Continuity mistake: Before one of Nameless' fights with Flying Snow, Nameless sheathes his sword and asks the army officer not to arrest her until their business is done. As the army backs away Nameless' sword is out and ready, and in the next shot he unsheathes it. (00:49:10)
Continuity mistake: While Broken Sword watches the Qin army leave with Moon, a strand of hair appears over his forehead in closeups but not wide shots. (00:52:10)
Continuity mistake: In one flashback Moon alone presents Broken Sword's sword to Nameless when he is driving away alone in a wagon. Just as he drives off, his ponytail switches from his right shoulder to his left. (00:56:45)
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: In the first stage of Broken Sword and Flying Snow's assault on the palace one soldier's shield is cut vertically by Broken Sword, then in the next shot the same soldier's restored shield is cut horizontally by Flying Snow. (01:09:05)
Continuity mistake: As Broken Sword and Flying Snow ascend the stairs to the palace, watching in slow motion proves that none of their blows actually land and none of the soldiers who fall down "dead" are wounded in any way. (01:09:45)
Continuity mistake: In the third rendition of the story of what happened at Zhao, Nameless shows that his attack could have immense precision by throwing all the additional sticks in the air along with the white one. Not only does the white stick change trajectory during the scene changes, but at the end the additional sticks all seem to fly in from a barrel just out of sight instead of falling all around Nameless' sword.
Continuity mistake: After Nameless' first attack on Sky (with spear still covered), the spear is shaking and the rope holding the cover to the spear is tied very tightly. In the next shot, when Sky goes to take the cover off, it's loose enough for him to slide it off without undoing the rope.
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.