I have an index of posts where I'm wanting to insert a Facebook Like button for each post. Thus far, I've set all Open Graph data in the head for single posts. Any ideas on using the open graph data (particularly, the thumbnail) within the loop?
Short answer: you can't do that, that's not what OpenGraph data is, does, or how it works.
Long answer: OpenGraph applies to the single post pages only, realistically. When you're putting a like button (for example) onto each post on a archive page, the like button is going to point to the permalink of the single post. That's where FB will look for the OG data for that particular like, not on the archive/home page.
Best answer: Don't DIY it. Just install my Simple Facebook Connect plugin, and let it do all the OpenGraph grunt work for you automagically. I just added support for Audio data, and I'm improving the video handling now. SFC 1.2 will have some great functionality there. :)