Mardonius has an attack named Perseus Arrow. Why a Persian would use the name of a Greek mythological hero (unless, you know, they made a flimsy Persian-Perseus association) is never answered.
The term "Spartiate" is used in the game as a sort of middle infantry between peltasts and hoplites. In real life, the name had nothing to do with the military field; it was a term for the upper class citizens of Sparta, who in fact were the ones who fought as hoplites in times of war.
Ahmose wears a royal nemes crown that should have not been worn by anyone other than a pharaoh. Inaros, for his part, wears a rather bizarre cobra hood-like headdress that seems straight out of the 2000 Frank Herbert's Dune miniseries.
Meritaton's name is anachronistic, as it contains the name of the god Aten, who fell out of favor in Egypt after the scandalous reign of Akhenaten almost a millennium earlier.
The usage of the "Medjay" term in the European translation is another anachronism, as the word fell in disuse after 1077 BC.
The game pictures the lost city of Elbo as being placed in midst of the Nubian jungle, when in real life it was supposed to be a man-made island.
In the game, the Persians have the ability to directly build ships with simple workers, while Greeks and Egyptians need to build shipyards first. Why the developers chose the Persians, the least maritime of those three civilizations, to give this feature, nobody knows.
Fate of Hellas calls "Cathai" to the region of India governed by Taxiles, which historically was the Punjab. Cathai, as odd of a choice as it sounds, was a medieval name given by Muslims to China. This probably comes from either a translation mistake or a honest confusion with "Cathaea", a name that ancient chronicler Strabo gave to a Indian region between the Hydaspes and Acesines rivers.
Military
The game's European translation calls the Spartan light troops "peltasts", a term that was only used in Thrace and Paeonia before The Peloponnesian War. The correct name for their Spartan equivalent at the time would have been "psiloi", which is used in the English translation. Ironically, the Greco-Persian Wars did see real peltasts in action, but those were Thracian mercenaries working for the Persians.
Persian noblemen can be equipped with Dual Wielding sabers, which has no historical basis and seems to be just a Shout-Out to the Immortals in 300 (although, ironically, this game's version of the Immortals cannot be equipped that way).
Some other weapons, like the Persian tri-dagger, are definitely made up.
Demaratus fights with a large labrys axe, which can also used by regular troops. In real life, the labrys was largely used for ceremonial purposes.
Among its weapons, the Egyptian civilization has the classical khopesh, which historically fell out of use around 700 years earlier. This is probably because, as in Every Japanese Sword is a Katana, it seems you cannot show ancient Egyptians in media without giving them that kind of sword.
In Fate of Hellas, the Macedonian light troop is the sarissaphore, a name that only applied to light cavalry. While you could pardon this previous point as a stretch of the word, the game also calls its heavy troops "hoplites", a term that didn't apply to Macedonian phalangites because they had abandoned the hoplon for a smaller shield named telamon or Macedonian pelta.
Characters
Although this can be pardoned as Acceptable Breaks from Reality to have him as a hero unit in the game, in real life Xerxes wasn't a Frontline General and most definitely would have not fought with a BFS. The same goes for his adviser Artabanus.
The game has Miltiades as the Athenian commander at the time of the Battle of Thermopylae, a strange choice given that the real Miltiades had been dead for nine years by that point. At the time the game is set in, Athens was actually led by Themistocles, who was the main driving force behind the Greek resistance against Xerxes in the first place.
Candaules seems to be an original character. That, or he is a time-misplaced Candaules, king of Lydia, who lived two centuries before the game's events.
Shabaka lived in the 8th century BC, not in the 5th. Oddly, the game itself has a preface commenting Shabaka would eventually become a pharaoh of the XXV dynasty, apparently hoping the players are not knowledgeable enough to know that this would require the game's Shabaka to travel 240 years back in time.
Wedjahor is apparently meant to be the historical Wedjahor-Resne, an Egyptian nobleman that betrayed his country for the Achaemenid Empire, but the latter died in 515, while his version of the game is alive several decades later.
There's a "Rajah of the India" whom Xerxes has to defeat to control their country. It's unclear whether this is supposed to be a historical character, likely either Bimbisara or Ajatashatru given the timeline, but none of those ever warred against Xerxes, who never marched against India in the first place.
Khabash wasn't a former slave as claimed by the game's sequel, but the governor of Sais (it's even entertained he might have been a Persian satrap Going Native), and certainly wasn't killed by Alexander, whom Khabash outlived.
Fate of Hellas bizarrely puts Taxiles, an Indian king who allied with Alexander, in the place of Porus, an Indian king who was enemy to Taxiles and opposed Alexander.
Events
The game portrays Xerxes being forced to travel to India and drown a rebellion against the Achaemenid Empire. Nothing of this happened in real life; he did have to crush some rebellions to consolidate his power, but not in India.
The timeline of the game has Xerxes' invasion of Greece happening at the same time as Inaros' rebellion, when in real life twenty whole years separated the two conflicts. In fact, Xerxes himself had been dead and buried for five years when Inaros revolted against the Persian empire, which by then was ruled by Xerxes' son Artaxerxes.
The real Leonidas never set foot on Egypt, while his version from the games does in order to help Inaros in Sais (he had been dead for 20 years by this point, and even if he wasn't, he would have been 80 years old). This effectively puts Sparta and Leonidas in the place of Athens and its statesman Cimon, who did deploy in Egypt to help the rebellion against Persia. The game also deviates from story by allowing this Greek force being successful, when in real life it was completely defeated and forced to return to Greece. The whole expedition was considered to be an ill-planned fiasco, in fact, and it was precisely one of the events that later discouraged Athenas from wasting its meager resources warring against the Persian Empire.
No source specifically gives the kidnapping of Inaros' fiancee as his main reason to rebel against the Persian empire. More importantly, in real life the rebellion was crushed by Megabyzus, who later captured and crucified Inaros, while in the games Inaros is victorious and kills Megabyzus. The choice of having the Egyptian campaign's final battle in Memphis is especially ironic, as the real battle of Memphis was a failure for Inaros and his Greek allies and marked the beginning of the end for their revolt.
The game also follows the pop culture trend started by 300 where the Spartans were basically alone in Thermopylae and had to sacrifice themselves to move the entire Greece to act against Persia. In reality, Greece was already united by that point, and the Greek contingent in Thermopilae included Spartans, Athenians, Arcadians, Thespians, Thebans, Corinthians and other peoples.
In the game, Demaratus and Hydarnes die in the Battle of Thermopylae. In real life, Hydarnes survived to the war and returned safely to Persia, while Demaratus' fate is unknown, with some authors dating his death as an entire year later.
The game's sequel, Fate of Hellas, features a completely fantastic arc where Parmenion kidnaps Alexander in revenge for the execution of his son.
Fate of Hellas also has the Egyptian Khabash revolting against Alexander the Great, when in real life he revolted against the Persian Empire, which also happened a few years before Alexander arrived to Egypt. We don't know how the relationship between Alexander and Khabash went, but the latter was seemingly in good terms with Ptolemy, the Macedonian ruler of Egypt, after Alexander's death.
