Guddno, A couple of observations that I hope will help. I think you have to encode every section between the &s where there are spaces (where you insert your own text for titles etc)! I thihnk these spaces are most of the problem and the secure link won't work while they are there. So I think your link should become something like:
https://www.facebook.com/dialog/feed?app_id=MYID&display=popup&caption=%20Check%20out%20my%20MyGame%20score%20of%20%24%22%26points%20&"! &link=http://mygame.com/&redirect_uri=http%3A%2F%2Fwww.facebook.com%2F&name=MyGame&picture=http://www.MyGamePicture.png&description=
Can%20you%20beat%20my%20score%3F
There's a return after description= which may or may not copy-paste and cause you trouble and you still need to encode the urls (in red) that are not encoded from your first post (I've done the facebook link - green - as an example).
Edit - I also noticed that you're missing an & between the facebook id and the display=popup (in blue)....