A blatant license, presumably done for the viewer's sake, is that Aristoteles and Ptolemy both use maps that have the countries' names written in Latin letters. The same can be said of Ptolemy's narration including the piece of info that Alexander died on June 10 — June, a month of the Roman Julian calendar that would not be used until three centuries later.
Oddly, Olympias' chamber showcases a reproduction of the sculpture known as the "Ram in a Thicket", a Sumerian figure that was buried in Ur around 2600 BC and would only be unearthed in 1928. It's hard not to think this is an incredibly subtle Casting Gag referencing Angelina Jolie's famous role in Lara Croft: Tomb Raider.
A big deal was made upon the film's release when some claimed the Persians' portrayal seemed tailored to evoke Arabs instead. Some of the complaints were a bit farfetched, such as showing turbaned Persians (which is not the case, as most Persians in the film appear to be wearing caps that are basically the correct type, albeit with oversized ear and neck covering that do give them a turban-like look),note Even if they were, the turban is a pretty universal headgear and would not be horribly out of place there either, especially given that the Achaemenid Empire had contact with Arabia and India but there are a glaring one that went unnoticed by many people: Darius' lieutenant, a man who would have been obligatorily Persian, gives once an order in Arabic, namely "yallah" ("let's go"), which his men understand. Realistically, the line should have been in Old Persian.
The name "Hindu Kush" is a monumental anachronism, as its earliest usage in real life was around 1000 CE.
In the movie, Indians and Persians are visibly disgusted by Alexander merely kissing Bagoas. In reality, hardline homophobic attitudes among those cultures only began after interaction with Christianity and Islam.
While Hinduism does contain some admonitions against homosexual contact between males in the Dharmasastras, they only refer to full intercourse (in the same way they disapprove non-vaginal sex) and have generally very light "punishments" on the act, being either a fine or bathing in cold water. Otherwise, there is abundant same-sex erotic art in Indian temples and palaces, as well as reports on rulers engaging in homosexual entertainments without problem. Ancient Indian guests, especially in a party and within an aristocratic context, would have been unlikely to see Alexander kissing an eunuch as any other thing than a goofy party stunt at the worst.
As for the Persians, again, Zoroastrianism does include a prohibition on same-sex eroticism in the Vendidad, but it's thought it didn't apply to eunuchs like Bagoas. Indeed, Greek sources claim that Persians had similar pederastic institutions and that it was perfectly routine for kings like Darius to have eunuch boys as well as women in the harem. Anyway, Zoroastrian orthodoxy only influenced a small eastern Iranian population at the time, especially not Persian emperors and noblemen who would have been in position to get away with anything. Herodotus also claims that Persian men kissed each other as a greeting (he does, however, say that kisses on the lips were only exchanged between equals, which can hardly be said about Alexander and Bagoas).
The film shows Alexander devolving into a lustful alcoholic after Hephaestion's death. The alcoholism is accurate, as Alexander reportedly was a hard drinker, but ancient historians specifically contrasted that with Alexander's restraint in "pleasures of the flesh".
Military
The film crew Shown Their Work by having the cast ride on horses without stirrups, as those were invented much later, but they still show horseshoes, which are similarly a medieval invention. This may simply be a concession to the health of the horses on set.
The film shows Gaugamela's battlefield as being desertic and dusty, when in real life the battle took place in the banks of the river Bumodus, which should make it much greener. In real life, none of the big three battles between the Macedonians and the Persians happened in such a terrain, as contrary to popular belief, West Asia isn't made of desert after desert.
The movie shows Persian archers utterly decimating the Macedonian phalanx blocks, to the point the viewer might wonder why didn't Darius order to simply keep firing arrows instead of making them stop to launch his chariots. In real life, arrows were nowhere near as effective as portrayed. Although the Macedonian phalangites were less heavily armored than their old Greek homologues, their long pikes massed together and held high into the air would have deflected a lot of arrows, and their shields and body armor would have stopped many other of those arrows that managed to enter, so most of the Persian kills would have been lucky shots in the gaps of the armor rather than absolute murder as in the film. The film also omits that Alexander had its own units of archers, so it's not like his army was exclusively a sitting duck in the exchange.
Scythed chariots were pulled by four horses, not two as in the film.
The movie's version of Gaugamela also shows a squad of Macedonians with swords who, judging by their large shields and their position between the phalanx and the Companion cavalry, are meant to be hypaspists. In real life, hypaspists were armed primarily with spears, not swords, which were relegated to secondary weapons. Frontline swordsmen weren't a Greek thing, and would not be so until centuries later, when the Roman Republic won a few battles against Hellenistic armies with them.
Characters
Aristotle at the time of his appearance in the film should be around 40 years old, while in the film he's played by Christopher Plummer, who was 75 at the time and was characterized with white hair and beard to look the part.
In the movie, Antigonus is portrayed as an officer in the Macedonian phalanx, when in real life he was in charge of the army's 7,000 Greek allies, who rarely saw frontline action.
Cassander, who is seen participating in the Battle of Gaugamela (331 BC) in the movie, did not actually arrive to the court of Alexander until 323.
The film has Cleitus the Black and Antigonus being the assassins that kill Parmenio. In real life, the deed was done by Polydamas, a friend to Parmenio whose brothers Alexander was holding as hostages, and Cleander, a local officer. Other versions have Polydamas and Cleander summoning two or three more people to be sure, those being the Thracian prince Sitalces II and, depending on the tale, either the officers Heracon and Agathon or the famous commander Menidas.
The movie has Hephaestion being the one who comforts Alexander with big words into returning after accidentally murdering Cleitus. In real life, it was Anaxarchus, a skeptic philosopher that was another friend of Alexander and in this case gets Adapted Out.
Events
The film shows the Lighthouse of Alexandria already finished while Ptolemy is alive, while in real life its construction only ended after his death, during the reign of his son Ptolemy II.
Dialogue implies Phillip revoked Alexander's banishment basically next morning, when in real life Alexander and Olympias passed at least six months in exile.
The two major battles preceding Gaugamela, those of Granicus and Issus, are not present, and are instead condensed into the one battle shown in the movie.
The movie makes it look like the Greeks first encountered elephants in India, with Craterus commenting beforehand that they are fabled monsters. In real life, there were elephants in the Persian army, which the Greeks found and captured upon defeating the Persians as soon as the battle of Gaugamela was over (they were going to be deployed along with the chariots, but it seems they were withdrawn before the battle due to fatigue). The same happens with monkeys, which shock Alexander and company when they find them in the Indian jungles. Not only they should be well known animals to someone who had studied under Aristotle, it would have been weird that there was none in the Babylonian palace's zoo, which in the film itself showcases zebras and lions.
In the film, Alexander meets Stateira after taking over Babylon, while in real life he did after he captured the Persian camp and gained her as a hostage after a battle.
The film also gives Stateira the famous instance in which Hephaestion is mistaken by Alexander, which in real life was done by her mother-in-law Sisygambis.
Porus' famous answer to Alexander after the Battle of Hydaspes ("How would you want to be treated?" "As a king") is also given to princess Stateira. Porus himself, or an Indian enemy general who should be him, does appear in the film, but he has no lines, and given that he manages to escape capture, there would have not been occasion to say the line either.
In the film, Philotas and Parmenion are executed well after Alexander has married Roxana. In real life, they had both been buried for three years when he met and married her.
The real Cleitus the Black was killed at the Persian satrapial palace of Samarkand, which is located in Bactria, modern day Uzbekistan. In the film, he dies significantly later, after the expedition has already arrived to India. The party in which he dies is hosted instead in a large Indian palace, where Alexander can even be seen sitting next to an important-looking Indian dude who is likely a stand-in for the historical Taxiles, his main ally in the region.
The extended cut shows Alexander visiting some Indian ascetics who are clearly meant to be the historical gymnosophists. In real life, he didn't actually visit them, but sent another of his philosophers, Onesicritus, in his place.
Alexander wasn't wounded at the Battle of the Hydaspes, but at the Siege of Malli, which took place afterwards. The film also portrays Porus being able to withdraw his army and escape, when in real life he was captured.
Coenus died of illness in real life in the travel back to Babylon, while the film shows him dying gruesomely in the Hydaspes when an elephant stomps on his head.
The Battle of the Hydaspes itself is also portrayed in a different manner than how it was, omitting the presence of the Dahae Horse Arches in Alexander's army and the participation of Porus' cavalry contingent, as well as making it a borderline failure before the final charge at the end instead of the more clear victory than it was in history.
The film places the mutiny at the Indian river before the Battle of Hydaspes instead of afterward, likely because, as mentioned above, the latter battle is conflated with the Siege of Malli, which did happen after the revolt. This has the effect of making it look like Alexander returned from India by his own will after being wounded, when in real life the mutiny effectively forced him to stop advancing and return home by the Mallian region.
The film claims Alexander took his expedition through the Gedrosian desert because it was the shortest way. This is inaccurate, as the shortest way would have been by sea, as his fleet did. Historians aren't sure why did Alexander take the Gedrosian route with his land army, but it's speculated he just wanted to see the meridional parts of the Persian Empire.
The film version of Hephaestion dies in Babylon, while his real homologue died earlier, in Ecbatana.
Historical chronicles are unanimous that Alexander wasn't at Hephaestion's side when the latter died, not arriving in time due to the swift of his illness. In the film, for extra drama, Hephaestion dies inadvertently while Alexander is speaking to him with his back turned to the bed.
The film has the aged Ptolemy admit to his scribe that Alexander's generals had him poisoned to put an end to all the conquests and future consequences. While some historians think that Alexander may have indeed been poisoned, none of them think that his generals were responsible. Being young and ambitious, most of them had few things to lose and a lot to gain from more campaigns, especially given that Alexander's intended next objectives (Carthage and Sicily in the film, Arabia in real life) would have been significantly easier and safer than his previous wars against the Persians and Indians.
