To what extent do you agree that Gatsby from The Great Gatsby is a tragic hero?

In some ways, Gatsby is a tragic hero. His "rags to riches" story is presented as heroic. He is portrayed by Nick as an innocent person, brought down only by forces beyond his control: the "foul dust". Like a tragic hero, he is brought down by a fatal flaw, which in Gatsby's case is attempting to repeat the past. Gatsby's death can also be seen as heroic; he died taking the blame for Daisy in Myrtle's death. Additionally, Fitzgerald's choice to show us Gatsby through Nick's eyes, rather than choosing a more reliable perspective, allows Gatsby to be elevated to heroic levels through romantic descriptions - "only Gastby ... was exempt from my reaction", "there was something gorgeous about him".
However, it could also be argued Gatsby is not a tragic hero. He is morally grey; we know that he is an adulterer, and it is implied that he is a criminal (as Tom says, "I picked him for a bootlegger the first time I saw him, and I wasn't far wrong"). Also, although his death is heroic, Gatsby does little that could be seen as heroic in life: the "rags to riches" story is presented as admirable, but we could argue that this pursuit of wealth makes Gatsby materialistic and selfish - remember that Gatsby's father is still penniless in Minnesota. Finally, Gatsby's dehumanisation of Daisy is far from heroic - he is more interested in his fantasy of Daisy than in Daisy herself, as we see in the scene where he shows her the green light: "Daisy put her arm through his abruptly but he seemed absorbed in what he had just said", and in Gatsby's description of Daisy's voice: "her voice is full of money".