In the Jinsha battle scene, just before the Yang patriarch faces the Tartars' army of archers, the golden blade of his staff is (inadvertently) hacked off by one of the Tartar soldiers. In the next shot of Yang, the blade is still attached to his staff.
The film's story takes place during the Song Dynasty of China which lasted from year 960 to 1279. Yet when the 5th Yang insists on having his head shaved at the Temple, the monks are using a straight razor which was not invented until the 1700s.