Sorry for the delay in getting back to you. The HTML on your site has multiple, major issues. I'm not sure if they are the direct cause of the problem, though they could be and should definitely be fixed.
If you open the source HTML on your page in your browser and search for "<html", you'll see that there are 4 instances of that tag. There should be only one. Having it multiple times tells the browser and any Javascript that's running that there are actually 4 webpages contained in the response.. which is completely invalid. It's very likely that this is confusing the Javascript from each of the social networks and causing them to erratically display the buttons.
There are also additional inclusions of the body and head tags after each html tag, but I'm confident they're all from the same problem. Unfortunately, I don't have any idea what's inserting those extra tags, but hopefully pointing it out helps you narrow things down.
If you need more help, let me know. We'll try to help how we can, but this is not being caused by JFBConnect.
Thanks,
Alex