Alex,
I think there's a few issues. Basically, there's multiple extensions on your site that are including the Facebook Javascript library. This should have been called out with the Autotune Error Checker as well. You'll need to investigate and remove the extra calls where possible.
To do so, open the HTML for the page and search for "all.js". It should only be there once, if possible. On your home page, it's being included 2 times (the 2nd time is also using a different Application ID than what you set in JFBConnect). On the Zap calendar page, it's there 3 times. One time is definitely from Zap calendar. If they have a way to disable Facebook integration, even temporarily, I'd try it to see if that helps.
Finally, the code for the login with Facebook button is actually being replaced properly. I can see the right code in the HTML for the button. It's just not displaying because Facebook's Javascript isn't executing properly, likely from the conflicts above.
Hope that helps explain,
Alex