It didn't really strike me as unfaithful to the original opus tbh. The biggest flaw is that the siege itself feels like a short battle when it was supposed to last a decade (but then it's a common flaw in such movies, the sieges in LotR also last a night or two apparently). The lack of supernatural may be an issue but after all it's not like gods were wandering the battlefield in the Iliad as far as I remember, they were just "helping" from afar so the perception of the warriors wouldn't be that different from what we see in the movie (and by desacrating Apollo's temple, the movie did show which side some gods were on).
Also the major plot of the Iliad was mostly about Achilles making a fuss and bickering with the several kings taking part to the fight, which is well described in the movie.
I do think the writers of the movie knew their classics, even if they had to write a script that is hollywood-compliant. There are subtle references here and there (maybe it's a coincidence, but Odysseus/Ulysses throwing his spear back to Achilles when he asked him to join is probably a throwback to the part of the original story where Achilles dressed up as a woman to avoid a war he knew would kill him, and Odysseus outed him by throwing him a spear that he grabbed in mid-air).
I wouldn't say the movie claims to be a transcription of Homer's poem, but for a pop-culture interpretation, it's definitely not that bad.
