Titanium Mobile 1.6.0 (currently in its release-candidate stage) contains an upgraded Facebook module which uses new authentication features on both Android and iOS as well as a new set of methods to retrieve and submit data. Our new API documentation won't get generated and put up on the site until 1.6.0 actually ships, but until then you can peruse the "raw" version of the docs in our Github repository. Some sample code is included therein as well as in the latest KitchenSink Facebook examples (search for "facebook" when you get there).
Our iOS and Android implementations both use Facebook's OAuth 2.0 authentication scheme, as Facebook has deprecated all other forms of authentication. Y