In The Great Gatsby, what you refer to as Gatsby's moral ambiguity is the result of his obsession with recapturing the past as he sees it. Everything else is subservient to his dream. He does whatever it takes to win Daisy. The ethics of partnering with the man who fixed the World Series seems nothing to Gatsby, if doing so will put him in a financial situation that matches Daisy's current financial situation. His business practices further the main plot in the novel, as well as the main theme.
Secondly, his moral ambiguity contributes to the theme of the American Dream. Gatsby achieves it, but at what cost? What does his moral ambiguity suggest about attaining the American Dream? Is Gatsby's way the only way? Or is it a decent way?
Thus, Gatsby's morality, or lack of it, contributes to his attempt to recapture the past, as well as to the theme of the American Dream.
Gatsby's moral ambiguity is so significant because Fitzgerald's masterpiece is a microcosm of life in America in the 1920s. You can't really put 10 years into a book of 220 pages, but this comes close.
An indicative feature of the era was a coming out of women: the flapper's independence, the fast and easy lifestyle, and the right to vote. Likewise, prohibition reflected the moral quest of the conservative, while the speakeasies and underground drinking establishments demonstrated the rebellion of the young. Entertainment, spending credit and fun are all aspects of that era that we can't lose because we need to learn from it.
If Gatsby wasn't a character that wandered and waded in and out of all of this mess, this book wouldn't be as popular and it wouldn't teach what it taught. The central struggle is on a failed relationship with Daisy. This work reveals the wake left by his quest hurt many others as well as himself. So, all these aspects of the 1920s are things to watch out for. They are ideas to store and make sure we don't act the same for fear of what material items could make us do. We need to worry about what ambition makes us do.
His moral ambiguity makes readers think and question and analyze themselves.
Just to underscore what has already been explicated, Jay Gatsby's moral ambiguity is also what makes him a tragic figure. As such, Gatsby's search for his skewered and illusive American Dream becomes poignant. And, this poignancy is what renders Gatsby the tragic victim of the social arrogancy of Daisy and Tom and the others. This poignancy is also what causes Nick to tell Gatsby,
They're a rotten crowd.You're worth the whole damn bunch put together!
and Owl-Eyes to say at the funeral when so few attend, "The poor son-of-a-bitch."
Clearly, the tragic figure of Jay Gatsby becomes a prototype for the many figures of the materialistically driven Jazz Age of the 1920s, who, like Gatsby had ill-gotten gains that propelled them, they believed, into the sophisticated, moneyed world. As such a prototype, Gatsby's tragic character also furthers the theme of Appearance vs. Reality as well as that of the illusiveness of the American Dream that may not necessarily be attained by ill-gotten gains.