Let's ask for their political party so we can control for it in our prior probabilities of global warming wackery.

Well, it's somewhat (weakly) relevant; someone deeply embedded in an anti-AGW tribe who parrots the standard line without thinking too much about it, is being less rational than someone in a pro-AGW who comes out strongly against their tribal position.

My mad Google-fu turned up http://www.science20.com/science_20/democrats_dont_understand_economics_says_one_study_do_understand_compassion_says_another for you.

Quite a bit: This article discusses some of them, but ignores others. There's some interesting data if one looks at the GSS data which suggests that in the US, self-identified moderates are actually often the least likely to understand basic science.