Update: So we just got a chance to download and play with the app a little -- and just like the Twitter app, things don't seem to be quite fully baked at launch. We couldn't get anything of the tabs to load apart from our personal photos, and there wasn't any confirmation when we sent in a Zune music status update -- although it did show up on Facebook, so it obviously worked. The photo viewer lets you leave comments, but you can't pinch-to-zoom -- or zoom at all, actually. We're sure Zune HD owners will be happy -- it's free, after all -- but we're going to assume Microsoft and Facebook have something far better planned for Windows Phone 7 Series.
Update 2: It's not just us -- the official Zune Twitter account confirms that the Facebook app is "experiencing some issues accessing data." We'll let you kow if we hear anything else.
Facebook app now available for Zune HD
[Thanks to everyone who sent this in]