You could easily change the title of the "The Calydonian Boar Hunt" to "The Tragedy of Meleager." Really, this (almost) invincible hunter is the main character of the tale, and like many tragic heroes despite his general awesomeness, he eventually brings about his own downfall.
According to Aristotle, every tragic hero is supposed to have a hamartia. This idea is often mistranslated as a tragic flaw, but a more accurate translation of the concept is "a missing of the mark" or "error in judgment." For Meleager, this is sparked by his affection for the huntress, Atalanta.
Despite the fact that he's married, Meleager totally has a thing for Atalanta and insists that she come on the hunt. The fact that the rest of the guys don't want her around doesn't bother Meleager one bit. Atalanta, who is a totally awesome huntress, draws first blood on the boar, and Meleager again insists that she be awarded the hide of the boar for her feat. His uncles protest, but Melager does it anyway.
Whatever his motivations are, it's probably hard for most modern readers to fault Meleager for standing up for Atalanta. You could see him as being unexpectedly enlightened for his time. However, it could be argued that Meleager kind of crosses the line when he slays his jealous uncles for taking the hide from Atalanta.
Whether you think Meleager goes too far in killing his jerky uncles or not, there's no arguing with the fact that this action is what causes his death. Meleager's mother is furious that her son killed these men who were her brothers, so she throws a log on a fire, which the Fates decreed would take Meleager's life with it once it was burnt to cinders.
So, in the end, you could say that Meleager's hamartia is his infatuation with Atalanta, his violent temper, or some combination of the two. Whichever way you shake it, though, it's clear that Meleager falls into the classic mold of the Greek tragic hero. He rises high, only to bring himself down.