I did some sleuthing into how the "UltraNav" middle button on thinkpads works (and got it working with Picasa!) The normal implementation sends messages only to windows with scrollbars. Awhile ago, I tried to make Picasa pretend it has a Windows scrollbar without actually making one visible, and it seems to be darned near impossible.
But there's another solution. Apps without real Windows scrollbars (like Picasa and Internet Explorer), can tell the driver to override its default behavior and use WM_MOUSEWHEEL messages instead. Why they don't do this globally I can't tell...there are some funny notes about smooth scrolling that may be the reason. So, IBM ships a driver with this setting overridden for many popular programs, like Acrobat, IE, Outlook, etc., but not Picasa.
You can, however, make the edits by hand, and then reboot to see them in action:
1. Open C:\Program Files\Synaptics\SynTP\tp4table.dat in notepad
2. Add the following lines to the "Pass 0" section:
; Picasa patch!
Some documentation online seems to say that C:\Windows\System32\tp4table.dat is the correct location, but editing it on my system didn't appear to do anything, whereas the Program Files location did.