If we are speaking to stereotypes of queerness, I don't think we will find it in Max. Yes, he has moments where he may fall into a few assumptions our society has about gay men, but for the most part, he is anything but our average gay guy. Just by looking at him, we can not assume Max is gay. This is not to say that we should do that for anyone, but if we are being realistic, we have to admit it does happen.
The thing about Max is that he is hilarious, but not in the flamboyant, girly kind of way that we see in many characters portrayed as gay men. For example, there are very few gay men on the show Sex and the City that don't fall into the stereotypical gay man persona. On the other hand, Max is a character that relates to a whole spectrum of men, not just gay or straight men. I understand the show Happy Endings is a sitcom with some unrealistic situations, but when it comes to Max, he portrays a real person to me. He's a guy's guy that is in fact into guys. He demonstrated what may constitute as "heterosexual practices" such as like sports and being extremely crude. In addition, Max is afraid of commitment which is something many women would joke about being an issue for the typical straight man.
And if you watch the show, you would know that Max may not be the most "queer" of the men on the show. His two best friends, Brad and Dave, act in ways that we might not expect of a straight man, crossing the line "between being a man" and being too in touch with their feminine side. All three men on the show in fact show us a type of "fluidity" for what it means to be a straight man as well a the gay character on the show.
P.S. I agree with Jill, everyone should watch this show!