I assume it would be full of attempts from both sides to provide proofs, counter examples and lot of external links to existing materials on the web (a good argument could for instance increase the rank of an external page if we cared to keep track of such metrics). You're right, ideally it would score something close to the center of true/false scale (whatever number we assign it) but things like imbalance of count of participants on each side could create a biased result.

I really like the idea of upvoting a part of a argument and not the whole. I have also thought about inter linking of statements which is useful to keep each discussion within some bound.