As it turns out, you can actually delete wall posts and comments (on your own wall or ones you created) as well as archive messages all by swiping away the item in question. Both left-to-right and right-to-left gestures seem to work, though left-to-right is a bit more reliable and natural.
Note: The gesture doesn't work everywhere - for example, it didn't work when I tried to swipe away a post by page (Android Police), probably because it still uses the old layout. Your mileage may vary, but in general you'll find the gesture working in most places.
Just like pull-down-to-refresh, this feature is common in iOS apps and is easy to implement using the iOS SDK. Because the Android SDK doesn't make it easy at all, it feels quite a bit hackier and unnatural (let alone totally unobvious). Still, considering I thought there was no way to delete anything outside of logging into Facebook in the browser, most Facebook users should find this hidden capability handy.
Now, how about putting things like this in the changelog next time, Facebook?