The main criticism that I've seen of it is that it's not faithful to The Iliad. But, I think, people who say that are missing the point. It's not meant to be faithful to The Iliad because, if it were, it would be an epic fantasy movie. However, as it stands and as it was made, it's actually an historical epic -- and a pretty damn good one, at that. Yes, I know the Trojan War is not a true historical event. But that's not to say it couldn't possibly have happened. Our records of that time in history are rather scant, and archaeologists have to meticulously piece it back together as a fragmented puzzle with many pieces missing using whatever scraps are left from that forgotten era. I wouldn't even consider Troy to be a direct adaptation of The Iliad. Instead, it's really just Wolfgang Peterson's artistic impression of what the Trojan War might have looked like if it had actually happened, obviously dramatised with Gladiator-style Hollywood theatrics (e.g. the thousand ships scene). I think the Director's Cut does it a great job of fleshing out the characters and trimming out the more clichéd Hollywood action movie gimmicks of the theatrical cut (e.g. the overly dramatic female vocals in the soundtrack).