One thing you can do is get JFBConnect configured how you want and move those changes as you already are to beta and then www. Run Autotune on each of the sites to get the 'right' values for Autotune. Then, just don't copy the #__jfbconnect_config table to the new site(s).
If you are still tweaking JFBConnect a lot, you can make the following changes to the Autotune values or your Facebook App:
Domains: whatsyourtune.com (just leave off the subdomain of dev, beta, or www entirely)
Site URL:
www.whatsyourtune.com
With those settings, Facebook authentication should work on all of your sites. The issues you may run into (if you don't want to re-run and configure Autotune each time you move)
The De-Authorization Callback URL is the only one you could have some minor issues with. That URL is 'pinged' by Facebook whenever a user de-authorizes (uninstalls) your app. All JFBConnect does with that right now is lets you know in the Usermap area all the users that have done that (they still have accounts on your site). If Facebook is pinging the wrong URL (dev or beta), then that feature won't work. So, you can either re-run Autotune on the Live site, or just live without seeing who uninstalled the app.
I hope that helps explain, but if not, or you have any questions or are seeing real issues, just let me know.
Thanks,
Alex
Issue between localhost/dev/beta and live website
