What are the qualities in Gatsby that confirms the word "great" in the novel's title in The Great Gatsby?
Gatsby's greatest qualities relate to this ability to persist in his innocence and to believe in both his dreams and himself.
Nick recognizes and comments on Gatsby's penchant for dreaming repeatedly, seeing in Gatsby an person of unique abilities of faith.
Gatsby as an exceptionally romantic hero and a hopeful dreamer.
This faith is what makes Gatsby great. It is what sets him apart from everyone else. It is what lets him believe himself when he says that it is possible to "repeat the past". This tendency for hopefulness is also what leads Nick to surmise that Gatsby believes the world is "founded securely on a fairy's wing".
Importantly, Nick sees some innocence in all of Gatsby's dreaming. Only someone with a fundamental innocence could believe, as Gatsby does, in the inevitability of his own success. Only a great (even an amazing) innocence could shape someone into a Gatsby.
This is why he is great. Despite his flaws, his wealth, and his questionable morals, Gatsby is able to believe in a dream and hold onto some basic innocence.