Factual error: When they first assault the city, the Greeks construct catapults. Only problem: catapults were invented at 400 - 300 BC, i.e. about 800 years later; and the first models looked similar to giant crossbows. The one-armed onager and similar types (as seen here) were a later Roman invention.
Factual error: Chinese men are shown in the Trojan marketplace wearing Manchu-style clothing, something they would not wear until the Chin Dynasty (late 17th century until the early 20th). Also, there are no records of the Chinese ever traveling to the West during the time period of the Trojan War (circa 1000 B.C.).