It seems that the greatest evil is that which is inside Gilgamesh himself.
Humbaba is called the "Hugeness," and our characters' descriptions call him "evil," but Humbaba's actions to not really support this. I guess he is evil in the way something like Circe in the Odyssey or the dragon in Beowulf are evil: as a holdfast. That is, their very presence stifles a community by not allowing them to grow or challenging their dominant ideologies. Identity is important in an age of expansion. Perhaps this challenge to (national) identity is the definition of "evil"?
In this way, too, Gilgamesh's actions at the beginning of the epic threaten his community: he cannot control his passion -- his lust for women and his desire for combat. Gilgamesh must learn to temper the great bull inside of him before he can become a strong leader.
Even the people who are drowned by the flood are evil: they are simple noisy and annoying to the gods.
"Evil" in Gilgamesh is subtle, like it is today. It does not seem overt, so it challenges us to look inward, at ourselves and our culture.