Just discovered that Facebook’s link-sharing API doesn’t like links that aren’t URL encoded. This means that in cases where SWFAddress is used you’ll get funky results due to the necessary hashtag (#).
So links can be shared in Actionscript via:
var url:String = "http://www.facebook.com/sharer.php?u=" + encodeURIComponent("http://www.mysite.com/#/whateva");
var request:URLRequest = new URLRequest(url);
UPDATE: Actually, it wasn’t very friendly with this, either, so I ended up using bit.ly’s API to shortcode the URL before passing it to Facebook.