According to legend, Achilles' only vulnerable spot was his heel, where he eventually was hit with a poisoned arrow. The movie shows how such a legend can arise - when the soldiers first come to Achilles' body, he has pulled out all of the arrows in his chest and the only one visible is the one in his heel. See more...
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This film is loosely based on the Iliad, not a direct copy. As such, any book/film differences aren't valid. If you're interested in the "facts" of the story, such as they are, check them at the Wikipedia.
Continuity: During Achilles and Hector's duel, in the wide shot Hector uses his shield to shove Achilles' spear tip down to the ground, beside his right foot while his left foot is way behind him. However, in the next close-up as the spear tip is still on the ground right behind Hector's left foot, his right foot comes forward to snap Achilles' spear.
Continuity: When Priam, Paris, Glaucus, et al, arrive at the beach to see the Greek's 'Trojan' horse, the men who lie dead all over the sand change position. Particularly, in the first shot as it pans towards the horse, the two dead men in red lie on the sand in front of Priam a good distance away from the horse. In the next two close-ups of these men (the same two bodies), their positions are completely different. Then in the next wide shot, those two bodies are much closer to the huge 'Trojan' horse now.
Continuity: After Menelaus dies, during the Greek charge Hector spots Ajax doing his thing and the rolled white tourniquet around Ajax's leg wounds is clearly visible. When Hector rides toward Ajax, he promptly knocks Hector off his horse and the tourniquet is once again visible, only now it's wider and tied differently, and changes again within the following shots.
Continuity: When Menelaus bursts into Helen's room, as he confronts the handmaiden about her whereabouts, Menelaus' hair curl is in front of his shoulder when the shot faces the woman, but not when the shot faces Menelaus. The same thing happens with Paris when he is with Helen, with Glaucus when he says goodbye to Hector, when Hector speaks with Lysander at the armory and so forth. Throughout the film all the men's hair in front and back - its position, neat or not, curls or not, etc., noticeably changes between shots.
Factual error: When King Priam is showing Paris the Sword of Troy we get a close-up view of the blade and it looks suspiciously like steel or polished iron, as do a lot of the weapons which we see in this film. However, at the time of the Trojan War, civilization was still very much rooted in the Bronze Age and iron weapons would not have been available. Iron weapons were first used by the Philistines around 1100 BC, some years after the Trojan War, and it was still another several hundred years before this technology was ever used.
Continuity: At the start of the first battle when we see Achilles' soldiers penetrate the sands of Troy, Achilles throws a spear through a guys head. But if you look closely at the previous shot, the soldier's body is side-on, obviously so he can shoot the arrow, yet when it cuts to the spear going through the head, the soldier is completely facing Achilles.
Continuity: When Briseis runs to Paris and shouts, "Paris! Don't!" in the wide shot, Achilles limps near the dead soldier on the grass. When Achilles is hit with the final arrow he drops to his knees and behind him an arrow lies on the ground (it is the 2nd arrow that hit him, which he pulled out and threw), opposite the dead soldier, which was much farther back in the previous wideshot of the grass.
Continuity: After Agamemnon's death, Achilles kills the two soldiers to rescue Briseis and in the close-up as he starts to lift her, the soldier's helmet lies near his head by the steps and the sword's grip at his fingertips. In the following shots the body, sword and helmet all change positions, the helmet moves at least a foot and the sword moves a few feet.
Continuity: After Paris is given the sword of Troy, it cuts to Hector speaking to Andromache. In this wide shot the cloth draped small bed between the two large columns is turned at a slant. Yet when Hector leaves their room (before encountering Helen), the bed is now parallel to the short wall (which faces the sea).