Meyer Wolfscheim is nothing more than a stereotype. One has to wonder if Fitzgerald had used an Italian and described his big Roman nose if people would have complained about this description being racist. After all, a stereotype of the Sicilian mobster could just as easily been used sincemembers of both ethnic groups were heavily involved in organized crime. One huge Jewish name was Meyer Lansky; the coincidence of the first name of Wolfscheim and Lansky brings verisimiltude to the narrative.
I think that Wolfsheim's relationship to Gatsby shows the seedy side of Gatsby's character and, for the most part, Wolfsheim's function in the novel is to color Gatsby's character.
Several facets of Gatsby can be seen through Wolfsheim. Gatsby's naivete is demonstrated when he introduces Nick to Wolfsheim without realizing that this man does not jive with the picture he has just painted of himself when speaking with Nick in the car. Instead of being an "Oxford man" coming from old money, Gatsby is now seen as having underworld connections with people who fear and praise him in a rather undignified way.