Wott first of all, thanks for a GREAT plug-in! And I can see why one would like to run support on ones own site but then at least make it searchable or have a forum!
I’m not using MU but managed to fix it on a single install, if you look at the code in picasa-express-2.php line 233 we have this line:
if (!current_user_can('picasa_dialog')) return;
This means that if the user don’t have the privilege picasa_dialog then the icon will not show up. If you use for example “User Role Editor” then you can give a role that privilege and it should work.