In the tea scene, Mulan is seen clearly pouring tea into the four teacups, but when the Matchmaker kicks up the table, the hot tea magically disappears into thin air as the cups fly up.
When Mulan is bathing in the lake her face goes from dirty to clean, dirty to clean and then once again.
When Mulan rides off with her fellow soldiers to pursue those retreating, she goes in a straight line. When she looks back, Commander Tung and his army have disappeared.
A trebuchet is used against ground troops. Trebuchets are supposed to be used against fortified structures such as castles.
Several characters refer to the "Silk Road". This expression was coined by German historian Ferdinand von Richthofen in 1877, nearly 1000 years after the setting of the film. However, it could be argued that this is simply a convenient translation to modern English of a term that the characters were "really" using.
When Commander Tung meets with Mulan, he tells her that he knew Zhou, Mulan's father. If Commander Tung really knew Zhou, he should have also known that Zhou only had two daughters. However, Tung says "knew" instead of "knows", which means that he and Zhou lost touch long ago, most likely when Zhou retired from service due to his injury, which probably happened before Mulan was born, so Tung wouldn't know anything about Zhou's children.
When the imperial soldiers sally forth from their castle to meet the enemy, mountains appear and disappear in the background and inconsistently change distance or position.
Unlike the Greek phoenix, the Chinese fenghuang did not go up in flames to renew itself; it propagated in the normal way. While the bird is fictional and has no "real" biology, this movie makes a concentrated effort to get Chinese culture right.