Jay Gatsby is not intended to be a truly "great" person. Rather, this character is intended as a commentary, often ironic and prohibitive, regarding materialism and a corruption of American morals.
The title of the novel is indicative of this effort, positioning the book as a satire.
The elements of satire in the book include...the grotesque quality of the name “Great” Gatsby in the title.
Critics have commented on the origins of this novel with roots in traditional satires, stemming back to ancient Rome.
Originally, the title of the book was “Trimalchio,” based on an ancient satire of a man called Trimalchio who dresses up to be rich.
From this evidence, we can see that Gatsby is not meant to be seen as great in any actual way. He is to be seen instead as great despite himself, great because his dream remains somehow (and startlingly) uncorrupted by his materialism, his profession (as a bootlegger) and by the society he keeps.
Jay Gatsby's greatness can be seen essentially as a result of his failure to truly change. Gatsby never fully becomes the man he intends or pretends to be. In this failure, his innocence and goodness are preserved. This is true, at least, from Nick's point of view.
Through Nick, we come to see Gatsby as a muddled or accidental hero. Blind to his virtues because these virtues are maintained despite his aims.
His ignorance of his real greatness and misunderstanding of his notoriety endear him to Nick, who tells him he is better than the “whole rotten bunch put together.”