The best solution, IMO, is to use the browser as a platform: a Chrome extension can allow users to seamlessly sync data between services, because Chrome already has access both to your Facebook account and your Picasa account.
The best solution, IMO, is to use the browser as a platform: a Chrome extension can allow users to seamlessly sync data between services, because Chrome already has access both to your Facebook account and your Picasa account.
(I work on the Facebook platform.)
BUT - what if I actually want to export all of my photos into SomeApp.com, and I want to give SomeApp the right to store my photos indefinitely? Is there an API they can use to pull it from Facebook directly?
You can definitely export all your photos into SomeApp.com using the graph API and they can store your photos indefinitely. These APIs are documented at http://developers.facebook.com/docs/api.
When Facebook switched from their old API to their new OAuth-based API they also removed restrictions on storing data.