UPDATE Nov 2, 2008: If you don’t want to get into trouble installing Windows version of Picasa and happy to use F-spot instead, head over to the new article here.
The picasa application from Google repositories with Facebook button does not work for Facebook photo uploads. It ends up with a blank window with nothing but a link. However, I have found an alternative in Ubuntu Forums and it works.
The trick is to install Windows Internet Explorer under wine and then install the Windows version of Picasa. To do this, make sure you have wine installed and picasa removed from your system.
This is how you do it: