I think it's an interesting case on a lot of levels. Lawrence v. Texas kind of opened the way for this lawsuit when it held that under the 14th Amendment, morality alone couldn't justify the government's intrusion into the bedroom.
The ACLU has an interesting article on the subject for background purposes:
http://www.acluutah.org/bigamystatute.htm
At any rate, on an equal protection level (I don't know if this is discussed here), I can't really see how such a prohibition on polygamy in the cohabitative sense, could even be found to have a rational basis. How is it that it would be perfectly legal for married people to engage in orgies with other married people just so long as no one cohabitates... but if cohabitation happens, it's a third-degree felony?
I'm not one to stand in the way of encouraging swinging, but I'm having a hard time figuring out why the taxpayers of Utah would GAS whether polygamy was happening in their neighborhood.