Might be an idea to allow you to share your score to your timeline - a great way of doing this is via a screenshot, you'll need to write some code in Unity to actually take the screenshot, but the Unity SDK handles the upload of it natively.
You can see an example of this on our game (http://apps.facebook.com/uberstrike) pushing B at any time will post a screenshot to a specially created Facebook photo album and depending on how Facebook's algorithms are feeling will usually create a feed story about it too. (We were lucky enough to be on the early beta for the Facebook/Unity SDK)
You can see an example of this on our game (http://apps.facebook.com/uberstrike) pushing B at any time will post a screenshot to a specially created Facebook photo album and depending on how Facebook's algorithms are feeling will usually create a feed story about it too. (We were lucky enough to be on the early beta for the Facebook/Unity SDK)
EDIT: Also worth a look is the scores API on Facebook, it's incredibly straightforward to use https://developers.facebook.com/docs/games/scores/