It is not recommended to install an older version of Picasa. But for those who want to, here are directions.
Some changes that are known not to be backwards-compatible and will cause certain features to not work anymore with an older version of Picasa:
3.9.137.69: first version having G+ auto backup included. If you are installing a Picasa version earlier than build 137.69, you will want to uninstall Google+ AutoBackup since it will interfere with earlier builds of Picasa (note that Google+ no longer exists):
Go to the Windows Control Panel.
Select Programs or Uninstall Programs.
Find and select Google+ Auto Backup in the list of installed programs
Uninstall it.
3.9.137.118: first version using new Google maps API; since April 2014, the map won't work properly in older versions of Picasa.
Procedure:
Download older versions of Picasa here:
Disable your Internet connection temporarily. For most people it may be easiest to just unplug the network cable or turn off the WiFi.
You can also go to the Network and Sharing Center, find the adapter being used and disable it temporarily.
Double-click on the Picasa Setup program (Picasa39-setup.exe) and install Picasa as desired.
Start Picasa if you didn't run it from the install.
Go to the Picasa Tools menu > select Options > click the General tab.
In the Options General tab go near the bottom and find the Automatic Updates box and set it to Don't Check for Updates, then click the OK button.
Exit Picasa to make sure the settings are saved.
If downgrading from Picasa Version 3.9.137.141 (build 141) or later, the following steps may be necessary:
Start Windows File Explorer
Paste the following path into the Windows Explorer address bar:
Windows XP: %userprofile%\Local Settings\Application Data\Google\Picasa2\temp\
Windows Vista / Windows 7 / Windows 8: %LocalAppData%\Google\Picasa2\temp\
In the Picasa2\temp folder, look for a folder called LifescapeUpdater
If the LifescapeUpdater\ folder exists, delete it.
Paste the following path into the Windows Explorer address bar:
32 bit Windows: C:\Program Files\Google\Picasa3\Update\LifescapeUpdater\
64 bit Windows: C:\Program Files (X86)\Google\Picasa3\Update\LifescapeUpdater\
In the LifescapeUpdater\ folder, delete the currentversion.ini file
If downgrading from Picasa version 3.9.140.239 (build 239) or later, the following steps may be necessary to ensure you can upgrade again to the latest version
Start the Windows registry editor:
One way is to hold down the Windows key and hit the R key on the keyboard
In the Run box that opens, type: Regedit, then click the OK button.
In the left Column, Navigate to Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Google\Picasa and find the REG_SZ key "Installed Version"
Either delete the Installed Version key or change the last number to a smaller number. For instance if it is 239, change it to 238.
Exit the Registry editor
Restart Picasa and check that it doesn't try to update and that the Automatic Updates box is still set to Don't Check for Updates.
Exit Picasa again.
Re-Enable your internet connection by reversing whichever method you used to disable it.
Run a browser or something to make sure the internet reconnected successfully.
You should now be able to use the previous version of Picasa.