(at around 27 mins) When Nameless shows Sky's broken spear to Broken Sword and Snow, he had directed them to meet at midnight - yet when he leaves, it is clearly the middle of the day, as a building is visible in sunlight through the doorway.
(at around 27 mins) When Nameless comes back to Broken Sword after helping Flying Snow fend off arrows (as they comment on each others calligraphy and swordplay), close-ups of Broken Sword shows he has a piece of hair over his face. In the wide shots, his hair is swept back.
(at around 1h) In the scene where everyone is in white (the white calligraphy brush demonstration scene) there are positioning errors. Snow is on the right, Broken Sword is on the left. While Nameless faces them talking, he looks in the opposite directions.
At the beginning of the movie, subtitles state that China was divided into seven warring states. At the end, the subtitles then state that "the King of Qin" unified China, without specifying which one. Historically, the king that was the one to unite all of the Chinese states was Ying Zheng (later changed name to Shi Huang Di) who inherited the throne from his deceased father at age 13 (as opposed to the age of the king in the movie). At the time, Ying Zheng began to rule China, the seven states were already reduced to two larger states (Qin and Chu) which was later dominated by Qin when Ying Zheng was 22 years old. It is therefore impossible for the same king shown in the movie to be the king that united all the Chinese states, although the end-note is semantically correct.
On numerous occasions, it is possible to see the glue that molds the sides of Jet Li's wig to his head (it casts a plastic-like reflection in certain light). It's most noticeable during the fight with Ziyi Zhang("Moon"), when he traps one of her blades with his sword and there's a close-up of the side of his face, and at the very end, when he's reached the palace gate and turns towards the camera.
(at around 3 mins) At the beginning when Nameless first walks into the courtyard and the camera pans back and forth you can clearly see the line of soldiers is only a couple of people deep. It is possible to see daylight between their legs, however when shot is shown from above the fact the entire scene is filled with soldiers would have made this impossible.
The goof item below may give away important plot points.
During the end scene soldiers shot arrows at Nameless in front of the door. The next scene, the panning camera shows the arrows on the walls and the door revealing an arrow free region where Nameless was standing. First, the way the arrows are fired can not hit the walls horizontal to the ground as seen. Their tips should point downwards. Second, Nameless was not standing immediately next to the door but at a distance. Regarding this and the angle at which the arrows are fired, there can't be an arrow free region at a man's full height, it should be lower.