While we continue waiting for the root issue to be resolved by Facebook, I've become aware of a work around that should restore Facebook login and sharing functionality.
1) Log into Facebook.com from a PC
2) Under the "Account" menu in the upper right, select "Privacy Settings"
3) Under the "Apps and Websites" header in the lower-left, select "Edit your settings"
4) In the section "Apps you use" click the "Edit Settings" button
5) In the row for Photosynth, click the "X" on the far right
6) In the dialog box, click Remove
7) In the app, now log in to Facebook
This process will essentially reset the login path for the Photosynth app and get you out of the bad state that causes the all-white login screen. Panoramas previously posted to Facebook will not be affected by this action.
Hope this helps, and as I said, we are waiting for an official fix that will make this workaround unnecesary.
Eric and the Photosynth Team