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: Contrary to what is depicted in the mini-series, the concept of a "high king" never existed in ancient Greece.
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.).
Factual error: The siege of Troy occurred during the late Bronze Age, about 1,200 BC. Yet the weapons and helmets look like they are made of iron, which was to be introduced with the Dorian invasion some time later.
Factual error: In at least three places the Greeks use Roman names for Greek gods and persons. Ulysses is Odysseus in Greek, and Bacchus and Mercury are Roman names for Dionysus and Hermes.
Other mistake: Near the end of the movie, we can see that the walls of Troy have suffered heavy damage from siege equipment, probably catapults. Yet in the entire film, we don't see any siege engines. The Greeks haven't brought any on their ships, we don't see them make any in their beach camp and they don't have any with them when they try to storm the city. There's simply no indication that the Greeks have ever had or used siege equipment.
Factual error: In the Trojan marketplace where Paris goes to find his beloved black bull, South American parrots are displayed. Parrots of any kind were not introduced into Europe from the Americas until the 16th century.