Scott,
Thanks for re-posting and letting me know your version number. Hate to ask more questions now, but I must.
* What extensions are you integrating with? Or.. what (if any) profile plugins do you have installed?
* Have you added any custom code that integrates with JFBConnect related to profiles or anything of the sort?
I just re-read your post and saw that guest users were seeing that, which is a bit strange, actually. Generally, on a normal page load, we don't load anything from Facebook as that's just excessive calls and would slow the page down.. never good things. We really only try to get profile information during registration or a login.
Here are some settings that you can fiddle with that may fix the problem, or at least mask it (though that's not perfect either):
* Turning off Automatically Login Facebook Users - This can prevent a certain check of the user's cookie, which could be throwing that error, but I doubt it
* Turn off the profile picture in the JFBCLogin module - However, this would only affect logged in users
* In the Configuration area of JFBConnect, on the Facebook API tab, turn off the "Display FB API Errors on Front-end" setting. This will hide the error if it's enabled.
Finally, if you want, feel free to post (or private message) your site's URL and we'll see if we can recreate it.. and if so, see if there's anything on the page that could be causing it.
Thanks,
Alex