When a user without a WP account presses "Connect to Facebook" on the login page (wp-admin/wp-login.php), they wind up back on the same version of the page (login, not register), not logged in. My impression is that they should wind up on the register version of the login page, with a username and email address filled in for them, after which they'll be able to press the "Register" button.
However, a user with a WP account can use the "Connect this WordPress account to Facebook" button on their Profile page, and this works fine.
I'm running Simple Facebook Connect revision 377598 from http://plugins.svn.wordpress.org/simple-facebook-connect/trunk/ due to suggestions made in several other topics.
I've disabled all plugins except for:
* Simple Facebook Connect - Base
* SFC - Login
* SFC - Register
* Permalink Editor
I've also disabled HTTPS and set FORCE_ADMIN_SSL to false; this has not helped.
By adding debugging statements, I've determined that sfc-login.php:sfc_login_check() is getting an empty value for $fbuid, but it is not clear to me why. The sequence of HTTP requests when the user presses the "Connect with Facebook" button on the login page is:
(a session key, secret, and signature are passed back to WP)
I've replaced my blog's fully-qualified domain name with "myblog" everywhere above and also omitted the api_key.
There are no errors that are obvious to me in the requests and responses, and nothing in the output of WP_DEBUG (which I'm logging to a file) except for a number of "Undefined index: HTTPS in /www/wp3/wordpress/wp-content/plugins/simple-facebook-connect/sfc.php on line 39", which is just a harmless warning (plus an identical warning on line 209 of sfc-login.php).
I've tried this with Firefox 3.6.16, Safari 5.0.5, and Opera 11.10, all under MacOS 10.6.7; I get the same results with all browsers.