(This is noticable in several scenes). Achilles was dipped in the river as a baby, making him invulnerable to any injury (ok, except for his tendon/heel). So why does he have a scar on his left arm?
In the film I don't think he's actually invulnerable, he's just so skillful he may as well be invulnerable. At the end you'll notice he tries to take all the arrows out of him, but dies before he can reach the one in his heel. This could lead anyone who found him to believe the story of the river and his heel and whatnot.
The movie completely removes all of the "godly" influence and action of the original story. While the gods are mentioned, the movie really takes the stance that they were nothing more than a belief of the Greeks & Trojans. They myth of Achilles being dipped in the river Styx is completely dropped, and he is portrayed merely as an incredibly skilled warrior. This is why, towards the end, Paris is able to kill him by shooting arrows into his chest--Achilles pulls those arrows out, leaving just the one (first one shot) in his ankle/heel. Basically, the movie implies that this scenario is what lead to the "only his heel was vulnerable" legend.
I wanted to add something else as well. Towards the beginning of the film, when Agamemnon sends a boy to get Achilles for a one-on-one fight, the boy makes a comment along the lines of "They say you can't be killed." Achilles responds with "Then I wouldn't be bothering with the shield, would I?" That line alone demonstrates that Achilles wasn't invulnerable (in the movie), and therefore could be scarred & wounded.