2013-06-16 Update: There is now a patch for the issue discussed below.
I just upgraded to BlogEngine.net 2.8 as it contains a fix for broken links from Facebook. There were a couple of hitches that I'll share in case they help anyone else.
I messed up the first upgrade attempt because the updater utility updates the source folder (containing the newly downloaded 2.8 code) instead of the destination folder (containing the current version of your blog). This is a little odd and the result is I uploaded an unchanged instance and then embarrassingly complained the the Facebook bug hadn't been fixed. It had, just not in the folder I was expecting. I probably didn't pay enough attention to the instruction video.
Having got that out of the way I discovered that new posts were appearing with a bad link (to /.aspx instead of /blog-title.aspx). I rarely post using the editor as I have a home-grown post by email service running. After a bit of digging it turns out that prior to 2.8 you could leave the slug empty when creating a post but now this results in the bad link. Luckily there isn't much effort require to fix this, you just need to set the slug before saving the new post:
In the middle of playing with this my live site died and started returning a 500 error. No amount of uploading the working local copy would fix this. Happily Server Intellect have outstanding support and restored a working backup for me in the middle of the night. Thanks chaps!