What's wrong with using anecdotes to make a point?
In the context you put it, it's different. The way the previous poster(s) were using it was trying to imply that because they witnessed 1 bad polyamorous relationship/family, that they must be worse overall, which is not logical at all. For all he knows, every single other polyamorous relationship is better, but he just happened to see the one bad one (not to say this is true obv, just making a point). You can say using anecdotes is similar to polling - Would you trust a poll with a sample size of only 1 or 2 people?
Good point. I definitely wouldn't trust that poll if it was claiming to predict the outcome of an election. I think the difference in this context is it would matter to me who the one or two people are. If they are close friends that I know pretty well, then I feel like I could make a positive judgment about them. If they are some random person in the neighborhood that I don't really know anything about apart from gossip, then I wouldn't trust myself to make that judgment without more information. I think the main problem with DC's anecdote is that the real issue there is poverty. A family that doesn't believe in contraception and has 10 children will have similar problems, but not many people are advocating for limits on the amount of children a family can have, despite the apparent detrimental effects it might have.
Let's back up here for a second.
The title of the OP is "Opinion of the Polyamorous community", not "should polygamy be banned". Plenty of people think poorly of people who have three spouses or ten kids. There's no inconsistency there. The level of 'proof' needed to support your case is a sliding scale. Thinking something is a bad idea requires significantly less support than putting your preferences into law.
Secondly, I want to bring up part of my anecdote that keeps being ignored. My primary issue with my acquaintance's polygamist parents wasn't financial, it was emotional. Recall, that I noted that the children were used as pawns in the wives' bickering.
Plenty of us have lived in households with financial strain. I doubt any of us have gotten punished because their mother was ten years younger and was having more sex with Dad than the other wives.