Revealing mistake: During the battle at Troy, when Odysseus and Achilles are standing together surrounded by Trojan warriors, Odysseus lashes out with his sword and kills a warrior (just before Hector appears and challenges Achilles). If you look carefully you'll see that Odysseus merely swung his sword for show; it didn't connect with the Trojan warrior who fell dead.
Revealing mistake: Achilles takes the spear that he later throws at Hector out of a dead person's body, but the spear has no blood on it at all.
Revealing mistake: It's stated that Achilles has been killed. He then is shown lying face up on his pyre. But if you look closely enough (zooming in might help) you can see that he's still breathing.