I've looked everywhere, and I don't see where anyone else is having this issue, but I created a widget for logging in to FB as per U29 on a test site running the TechGo 1.0 theme.
I have permalinks turned on, so I had to turn them off to get the page ID for the registration page, which is 41. I put into the widget different variations, none of which work:
Out of curiosity, I turned off permalinks, but it still does nothing outside of turning into a finger when you hover over it. I went to another computer, and clicking it does nothing. I tried IE 9 and FF 9.01 both. I turned off the Execute shortcodes in widgets, which turned the code into text. I re-enabled it, and it becomes a button once again, but the same problem as before.