What are the flaws in the character of the heroes in The Iliad that allow them to meet the tragic events that they encounter?

The greatest warrior in Homer's The
Iliad is Achilles, and he has many character flaws that lead to his tragic
death.  At birth, Achilles was dipped in the River Styx which should have made him
invulnerable to all harm; Thetis, however, was holding the heel of his foot, so this
spot was missed, creating one area of weakness.  But Achilles lives his life as a grand
warrior, believing that his is invincible.  Achilles refuses to compromise with anyone,
and any actions that he perceives as being taken against him cause Achilles to become
enraged.  Such is the case when Agamemnon takes Briseis from him.  Achilles refuses to
have his army participate in the war and later does not accept Agamemnon's agreement as
an apology.  Once he does get involved, Achilles continually goes after Hector until he
finally kills him and then parades Hector's body behind his chariot.  Achilles breaks
all rules about the importance of giving men a proper burial.  After The Iliad
closes, Achilles does get his due--he is shot in the heel by Paris with a
poisoned arrow.  So, Achilles's past behavior based on his belief in his invincibility
has led to his downfall.