What three purposes does Meyer Wolfsheim serve in The Great Gatsby?

Just to put a different spin on things: it has always been
my opinion that the Wolfsheim character betrays F Scott Fitzgerald's blatant
anti-semitism. Here we have Wolfsheim, identified, in the most stereotypical ways, as a
Jew, who is the sleaziest and most nefarious character in the novel. He does his dirty
business deals through a cover company named the The Swastika
Holding Company. Really now. And this same man, though his knows Gatsby well and has
been doing shady business with him, refuses to have anything to do with his funeral and
prefers to remain anonymous. I think Fitzgerald's intentions are obvious. And I am not
alone. Here's an excerpt from an essay by Martin Hindus, Assistant Professor of
Humanities at the College of the University of Chicago:

F.
Scott Fitzgerald and Literary Anti-Semitism:A Footnote on the Mind of the 20's June
1947

I
recently read The Great Gatsby for the first time, and it struck me that in all the
praise of the book I had heard from both Jews and non-Jews, something important had been
omitted—that viewed in a certain light the novel reads very much like an anti-Semitic
document. It is an excellent novel, no doubt of that, and part of its appeal is that the
reader knows (though he may be unable to define his knowledge) that the story and the
characters are general and representative rather than particular and confined.
Fitzgerald has written a tragic satire on American civilization, with the implicit
invitation to disentangle the idea of which the personages and events are outward
symbols. The individuals portrayed stand for the classes (but not in the Marxian sense)
to which they belong. That is nothing new: the same is true of every serious literary
work of art.

The Jew who appears in The Great Gatsby is not
the villain of the piece, but he is easily its most obnoxious character. His name is
Meyer Wolfsheim. He is a gambler by profession. His nose is flat and out of both
nostrils two fine growths of hair “luxuriate.” His eyes are “tiny.” When he talks he
“covers” Gatsby with his “expressive nose.” We first glimpse him in a mysterious
conversation with Gatsby about a man named Katspaugh. When, at this point, the narrator,
Nick, comes in and meets him, Wolfsheim mistakes him for somebody else whom Gatsby has
mentioned and he immediately begins to talk of a business “gonnegtion.” That
“gonnegtion” runs like a theme through the whole book whenever Nick thinks of
Wolfsheim.

Of course, you are
free to draw your own conclusions...