This has been an interesting thread. Polyamory has been of great interest to me for a long time, probably because I have failed dismally at monogamy. By this I mean I have failed to have a happy relationship with a woman in a committed one-on-one relationship, or at least one where the happiness lasted for long, though the relationships (three in number) did.
First, I want to comment on a lot of what has been said so far, and the biggest problem I see is that posters are not describing polyamory as I think of it. They are talking about monogamous relationships that are twisted to include other people, with predictable problems. Like adding another person to an existing couple. Like open relationships that are basically agreed on cheating. And the essential problems with these kinds of arrangements arise from the rules of monogamy persisting into the polyamorous situation. If my spouse agrees to my shagging another woman, then it is implied that she has authority over me to the extent that such permission is required. And vice versa of course. And so on.
Another point is that polyamory is trying to exist in a largely monogamous culture. It's not so much the idea that it's considered "wrong", though that is a factor, but the absence of a support system that monogamous couples enjoy. If polyamory was considered "normal" then how many books would be written about how to get along in a polyamorous relationship? There would be generally accepted "rules" that didn't have to be hashed out anew in each case.
I'd like to describe a situation where polyamory might work, and work a lot better than our current system. In short, the relationship would be "put together" by a group of people that wanted it, but were all new to that particular group. It would be done in a framework of existing successful polyamorous relationships, and there would be professional advisors available to help. In short, what monogamous couples now have.
I'd like to set out how I think the polyamorous "marriage" would work and how it would be superior to what we have now, but this is long enough already. I'll see if there is any interest before proceeding.