It's really easy: Don't install the picasa for Linux thats offered in a .deb file on the picasa website. It works fine, but doesn't allow you to log into your picasa webalbums anymore. Something is broken.
If you already installed it. Uninstal it using Synaptic. Uninstall it with all user content,
Then go to the picasa website and download the version 3.8 for Windows.
The download fiile is called: picasa38-setup.exe
open a terminal
go to the download directory: cd /home/yourname/download
type: wine ./picasa38-setup.exe
answer questions and ignore any error. After that run Picasa and select your foto directories.
It will all work fine.