In terms of the myth as a whole, with respect to heroes, what is unusual about Hercules/Heracles' character?
Does Heracles maintain his heroic status after commiting many mistakes and crimes in his life?
One thing we need to keep in mind about the term hero is the difference between literary heroes and our modern day notion of what makes a hero.
In our modern world, we think of a hero as someone whom we would like to imitate, to pattern our lives after; perhaps a professional athlete like Michael Jordan or an excellent citizen like Martin Luther King, Jr.
When we think of literary heroes or heroes from mythology, we do not think in those terms. These sorts of heroes have lives that usually follow a commonly recurring pattern. They are often born under unusual circumstances; are often the children of divine parents (cf. Heracles, son of Zeus; Theseus, son of Poseidon); often, someone tries to kill them when they are born (Hera tries to kill Heracles); they grow up in a place different from their birthplace; they return from that place and defeat some sort of king, giant, dragon, or wild beast; then they become king and rule quietly for a while before ultimately losing favor with their subjects or the gods; eventually, heroes die under strange or mysterious circumstances.
Regarding the pattern described above, Heracles fits this pattern very well. He defeats all sorts of villains and strange creatures; at various points in his life he kills people (his wife and children; a guest named Iphitus) which causes him to lose favor with the gods. These sorts of wrongdoings are not unusual, nor do they change the fact that he is a hero in a literary sense.
One significant difference about Heracles that does not seem to appear in his biography is the aspect of kingship. Heracles would have been in line, it seems, to become the king of Thebes if he had not killed his wife Megara, who was the king's daughter. Heracles' labors were performed for Eurystheus, who was the king of Tiryns, but Heracles never becomes king there. So, with respect to the hero pattern, the office of king seems to elude Heracles. Perhaps becoming a divinity on Mt. Olympus at the conclusion of his life serves as the substitute for human kingship.