SPOILERS GALORE (no, I don't like the spoiler tags)
It's been years since I've read the Illiad, but off the top of my head:
1. The gods don't make an appearance at all, whereas in the original story, the war is entirely their doing and full of their meddling.
2. There is no attempt made to suggest that 10 years have passed... The war is over so quickly, the cuts and bruises of a girl taken captive on the first day of the fighting don't even heal by the end of it, and Hector's son remains an infant throughout.
3. Achilles, for all we know, might not even be invulnerable. He suggests he's not, anyway, and his death in the film is done in such a way that the arrow striking his heel is merely what sets him up for more deadly blows, not his death-wound... But it's the only arrow he doesn't pull out, presumably leaving the people who find his body to draw their own, incorrect, conclusions.
4. As mentioned, Agamemmnon dies at the wrong time. So does Ajax, who barely even gets any screen time despite being a hero of Achilles' and Hector's caliber.
5. A love story between Achilles and Briseis is invented, when in the book (IIRC) she's nothing more than a posession Achilles wants back, out of pride, not love.
6. No mention of the sacrifice of Agamemmnon's daughter in exchange for favorable winds, which is strange, because they do everything else to make him into a monster...
There's tons of other stuff... It'd probably be easier to list what things in Troy actually match the Illiad.