Why is Gatsby's moral ambiguity significant to the work as a whole?F. Scott Fitzgerald's The Great Gatsby

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.