Deliberate mistake: When Alexander is giving his pre-battle speech at Gaugamela, some of the shots are 'flipped', which has the odd effect of suddenly making all of the phalanx pikemen left-handed.
Factual error: Just before old Ptolemy starts telling his story of Alexander, at the very beginning of the movie, we see a shot of the famous Lighthouse of Alexandria. It's fully operational, which is a mistake because the building was finished during the reign of Ptolemy's son, Ptolemy II Philadelphos, some years after the first Ptolemy's death.
Olympias: You are everything Phillip was not. He was coarse, you are refined. He was a general, you are a king. He could not rule himself. And you shall rule the world.