Starting today, you can serve XML sitemaps off apps.facebook.com domain, and notify search engines about changes on your pages. Naturally, this works better for pages that display content without requiring logins.
The best way to showcase your Facebook application to search engines is to register your site with appropriate services:
Each one of those services allows you to register a sitemap that lists out all URLs that search engines might find relevant. Publishing a sitemap does not guarantee inclusion in the index, but it does facilitate it for pages not linked anywhere else on the Web. Facebook will serve any file with ".xml.gz" extension without interpreting it through FBML parser.
When your pages are updated, you can additionally notify search engines about this change by issuing GET requests to these URLs: