Coins are placed on dead characters' eyes before their bodies are burnt. Ancient Greeks placed a coin in the corpse's mouth, not on the eyes. However, the Trojan War occurred before coined money was invented (in the 7th century BC), so they wouldn't have had coins at all.
Most equipment used by the Greeks, such as the large round shields and Achilles helmet, is from the Classical Period (5-4th centuries BC). At the time when the epic is set, the Greeks used small bowl-shaped helmets and light leather shields shaped like the number 8.
When the Greek leaders are lining up to offer gifts to Agamemnon, one of them carries a red-figure vase shaped like a submarine. Red-figure pottery (made of red clay with a black glaze, from which lines and shapes are removed to make red images) was not made until the fifth century BC.
The main weapon used by foot soldiers in this movie is the pike. The earliest recorded large scale use of pike was started by Philip II of Macedon, Alexander The Great's father around 330 BC. These soldiers came to be known as the Macedonian phalanx. Trojan war was fought around 1260 BC.
Throughout the film, whenever Hector, Paris, Achilles, and Menelaus all draw their swords, metal scraping can be heard as they are pulled from their shields. However, the interior of the shields are lined with cloth, and the loops that hold the swords are leather, not metal.
When the boy goes to find Achilles to fight the warrior, he says "the Thessalonian is huge". He should have said "Thessalian". A "Thessalonian" is someone from Thessaloniki, a city that was founded centuries later (4th century BC) by Cassander, who became the king of Greece after Alexander's death. Cassander married Thessalonike, Alexander's sister, and named the city after her.
While Paris fights Menelaus for Helen's hand, their shadows are opposite, which means the sunlight was on both of their lefts as they faced each other. They do not match up; the scenes must have been shot at different times of the day.
When Patroclus is fighting Hector in Achilles' armor, Hector stabs him hard in the chest, which would make a hole or a least a cut in the armor. When Achilles goes to fight Hector in the same armor, no marks are visible.
When Achilles' ship hits the beach, several men are hit by arrows and fall into the surf. When the warriors move onto the beach and use their shields as cover, the ship is behind them, but there are no bodies in the water or on the beach.
When the soldiers go into formation on the Trojan Beach, a flaming arrow is stuck to Achilles' shield. In the shot from Achilles' point of view, the arrow is nowhere to be seen. As Achilles and his army move out of formation to attack, the arrow is directly in Achilles' line of sight.
When Achilles burns Patroclus' body, the moonlight reflects slightly off his arms. When ancient Greeks burned bodies, a person with a torch was always beside the one who placed the coins, so the firelight should've reflected off Achilles' arms as well. It doesn't, indicating that the scene was not shot continuously.
When Paris enters Helen's room after dinner, he gently pulls her hair so it all lies on her back, behind her shoulders, exposing her neck. When she gets up, it is around and in front of her shoulders. It could have happened while she got up, but after a quick shot to Paris, Helen's hair is once again tucked back behind her shoulders.
During Hector and Achilles' battle, Achilles kicks Hector to the ground, and Hector crawls towards a piece of broken spear. In one shot Achilles throws away his shield and talks to Hector. During this speech, Hector reaches the spear. After the shot of Achilles walking towards the camera, Hector just reaches the spear and gets up with it.
Achilles talks to the men right before Achilles and the Myrmidons take the Trojan beach. As the shots go between Achilles and the Myrmidons, the hundreds of ships that should be behind them suddenly disappear; only a bare ocean can be seen.
As Patroclus enters Achilles' tent to ask if he will join the Greeks to fight the Trojans, Achilles is seated while eating and drinking. In disgust at Patroclus, Achilles dashes the contents of his cup on the fire. Moments later, he drinks from the empty cup.
After the battle in front of the gate of Troy, the field is clean, including every scrap of flesh, every drop of blood, and every footprint. When Achilles rides up on his chariot to challenge Hector, it appears that some grass has been replaced.
In the Director's Cut, during the burning of Troy, a temple burns just after a statue falls forward and breaks. A crew member in a motorcycle helmet is on the roof, running across the top right-hand corner.
After the Achaean fleet is spotted, villagers from the countryside begin pouring into the city. Among the animals being lead away is a pair of llamas. Llamas are originally from South America, and did not exist in Troy.
When Paris fights Menelaus, the view from Paris' eyes makes it appear that Paris' helmet has no nose protection. Paris' nose protection, a slim piece of metal placed directly between the eyes, would not be visible by the wearer.
Achilles throws his sword at a Trojan; it lodges into his opponent's head. Afterward, he uses a sword to behead the golden statue. Just before Achilles threw the sword into the Trojan's head, he had one sword in each hand, and he only threw one.
Achilles kills Hector with a spear. When Achilles drags Hector back to camp, the spear sticks out of him. In the next shot, when Achilles is back at camp, the spear in Hector is gone. Hector was dragged for many miles, so it's very likely that the spear either snapped off or fell out by the time he reached camp.
During the battle in front of the gate of Troy, the dead are in a line where the two armies clashed. The dead are obviously rubber dummies based on how they move when stepped on. Also, no dead are seen towards the rear of the field, where victims of the archers would be expected.
When Paris fights with Glaucus before the gate of Troy, Paris' view of Glaucus is partially obscured by the shape of his helmet in front of his eyes. When Paris is shown from Glaucus's viewpoint, Paris's eyes are not covered by the material of his helmet.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
When the Trojans invade the shores at daybreak to initiate the second battle, it is quite obvious that Brad Pitt was playing the role of Patroclus until his throat was cut. First, you can clearly see Pitt's face in Achilles' helmet in the close-up shots when he is about to start fighting with Hector. Second, you can see the significant change in Patroclus' physique before and after Hector cut his throat.