The first one with the double links looks like something wrong with JFBConnect. In between /provider/ and /icon.png there should be the name of the actual provider, like /provider/facebook/icon.png. Can you let us know what social network the user is connected with and we'll gladly help investigate that further.
For the Facebook pictures, unfortunately, they've been restricting profile data more recently. Previously, we were storing a link to the user's profile image and would show that. Now, Facebook provides a temporary link only which expires after some time. Because of that, the link stops working.
We could refresh the user link when you load the usermap page, but that adds a lot of overhead to fetch each image.. and may not be worth it. We're considering what to do, but the picture in that section may have to be removed.
I hope that helps explain and sorry for the inconvenience,
Alex