During a sequence where time "stands still", one of the soldiers "frozen" in combat closest to the camera can be seen blinking.
It is mentioned three times that Troy is the gateway to the riches of Byzantium. The city of Byzantium was founded in 667BC five centuries after the Trojan War.
Early in the movie, there are Chinese traders wearing Manchu clothing in Troy's marketplace. No Chinese reached the Mediterranean before the Roman Empire and Manchu clothing wasn't used in China before the Manchu conquest in the 17th century AD.
When Clytemnestra kills Agamemnon in the swimming pool, her modern style bra and underwear are clearly visible through her wet clothes. Such undergarments were not available during the time of Helen of Troy.
South American parrots in a Trojan marketplace.
When a guard announces that the Greek Navy is approaching, people gets frightened and run everywhere. Among them is a man leading a group of Southern American llamas. Old Worlders did not see llamas before the Spanish conquest of Peru in 1532, and it wasn't until even later when the first live llamas were brought to Europe. Today, llamas are still not common farm animals in Anatolia.