Many heroes of ancient mythology don't always behave in ways we'd consider exceptionally heroic today. Hercules, for example, frequently kills people in rages and other episodes who don't seem very deserving of death. Odysseus of course has that whole thing with killing all his wife's suitors after being missing for twenty years.
I understand that the ancient idea of a hero was more of a person who was simply better than other man, and it generally isn't until the advent of Christianity that we find the newer, more modern idea of a hero where moral outlook matters as much (if not moreso) than physical strength or cleverness, with a health dose of self-sacrifice for good measure.
I'm interested in any further insight and analysis anyone could offer on the subject, as well as some reading materials as I might like to write an essay or two on the subject.
Campbell would argue that a hero never changes. Across cultures the pattern is very similar if not identical. Morality varies but the process of becoming a hero and ultimately succeeding is nearly universal.
I'm coming at this as a theatre historian, so others with more extensive work on the epics can provide a better point of view on those. The best source I can think to recommend is Aristotle's Poetics, though he is describing tragic heroes more than epic heroes. Aristotle is mostly concerned with how tragic heroes function within a specific form, but he argues that they should be consistent in their values and should come from the type of people one naturally expects to be heroic (he explicitly states that slaves or women would make illogical heroes). Nowhere in there does Aristotle suggest that heroes should be self-sacrificing or forbearing, though.
A couple of points, though, that I use to explain the difference to undergraduates (Less historiography than Intro to Lit, so if it has to go I understand.):
When considering Greek heroes, don't think of the word "hero" as it is in modern usage. Think "badass." Heroes are heroic by virtue of their accomplishments and unwillingness to compromise themselves for others. To modern eyes, Oedipus's problems really stem from him killing a bunch of people on a highway for a minor slight. To the greeks, his killing of Laius was perfectly natural for a heroic figure, and the only ill fate of the incident was that the man he killed happened to be Laius.
Consider how morality changes when you assume a society that is predominantly polytheistic. In societies where monotheism is the norm, morality is often measured according to whether or not ones actions please or displease the deity in question. In polytheism, there are some actions that enrage all the gods (the myth of Tantalus is a good example), but most of the mythology describes humans that pick a particular deity to please with his/her actions and accepting the displeasure of others.
Jason begins as a hero during the quest for the Golden Fleece. He has won the favor of the goddess Hera and she fights to keep him alive even as other gods try to kill him. His fortunes change later because of an immoral/impious act toward Hera; he swore an oath in her name never to leave Medea, and breaks this oath for personal gain. Hera turns her back on him, and he loses his children and new wife, and dies in disgrace.
Orestes is another interesting point. His mother kills his father, so he kills her. In The Eumenides (Aeschylus) he is put on trial for killing his mother. He openly admits that he has done it; his defense is that the requirement that he avenge his father outweighed the strictures against matricide. The Furies demand he be punished for the impiety of matricide, and Apollo argues that avenging a father is more important. The jury is deadlocked between the two and Athena (the judge) decides that the deadlock will favor Orestes's acquittal.
This play is part of Athenian civic myth, dramatizing the shift from a vendetta society to a judicial one. However, at no point is Orestes chided for having taken the life of another human being; the entire dispute is whether or not his actions that pleased one god could be exempted from the wrath of another set of deities.
I can recommend Joseph Campbell's book "Hero with a Thousand Faces", actually having read all of his work, I'll just say that it's an extremely fascinating read as a corpus.
Some time ago Bill Moyers interviewed him on this subject and this is also worth watching. There are also a variety of videos of lectures and presentations which, although less professionally produced, contain a wealth of fascinating information.