At first, I didn't feel much of a need to comment on the film, since so many others have written and have said so many things. But I think there are some really important points to made, and I haven't seen anyone make them. So here I am writing.
In my opinion, almost everyone misunderstood the relationship between Hephaistion and Alexander. In the modern world, especially in the West, two men are either very close to each other, sleep together, and have sex, or they keep a good comfortable distance from each other and, if they're friendly, might punch each other on the arm. In this film, we see a relationship that is hard for most people today to understand, namely a passionate love relationship between two men in which sex is not very important and possibly even absent.
Aristotle essentially explained the whole film near the beginning when he told the young couple something like the following, as best I can remember it, "When two men lie together in lust, it is over indulgence. But when two men lie together in purity, they can perform wonders." Or something like that. Given what I know of that culture, I am sure that "in purity" means no sex, or at least very little. That's why we never see them kiss. In the film, as in many older films, kissing is a metaphor for sex. Even when Alexander kisses his mother, it refers to the idea of sex. That's why Alexander kisses Bagoas, but not Hephaistion.
Now I'm not sure if the real historical Aristotle would have made that remark. That's not exactly what he says about homosexuality in the Nicomachean Ethics. But the remark is plausible enough since Alexander could easily have heard such an idea during his youth. Plato (before Aristotle) expressed that idea, and Zeno of Citium (after Aristotle) did too. So even if Aristotle never said this to Alexander, it is plausible enough that the idea was in the air and that Alexander heard it from someone or other.
Some have complained that the "homosexuality" (assuming that A's relationship with Heph. should even be called that) was thrown in their faces too much. But it's crucial to the plot. Stone is hypothesizing that Hephaistion was essential for what Alexander did. Further, it's a standard Hollywood convention to juxtapose a love story with some great political, military, or otherwise grand event. There are tons of examples. Titanic, Enemy at the Gates, Gone with the Wind, ... the list could go on forever. It really is homophobic to complain about Stone continually going back to this theme, because he has a perfectly good artistic reason to do it.
A few more details: Alexander's hair. I think that Stone was trying to make Alexander look like Martin Potter in Satyricon -- a nod to Fellini.
Alexander's accent and soft appearance. Another nod to a great director passed on, this time Stanley Kubrick. Farrel really looks a lot like Ryan O'Neil in Barry Lyndon. In fact, he really looks like a Ryan O'Neill / Martin Potter coalescence. I think it's deliberate.
The softness of Alexander's personality. In a lot of scenes it made sense. He was gentle enough to know how to approach Bucephalus and tame him without scaring him. He was open minded enough to adopt a lot of Persian culture and encourage intermarriage, while the other more "he-man" folks around him were less comfortable with the idea.
Yes, if you haven't figured it out by now, I do like the film. People's hatred of the film is hard for me to understand.