Same here (using WP 4.0).
Some logs to help you digging:
PHP Fatal error: Uncaught exception 'Exception' with message 'Authentication failed! Facebook returned an invalid user id.' in DOCROOT/wp-content/plugins/facebook-publish/lib/class/hybridauth/Hybrid/Providers/Facebook.php:286
Stack trace:
#0 DOCROOT/wp-content/plugins/facebook-publish/lib/class/hybridauth/Hybrid/Endpoint.php(725): Hybrid_Providers_Facebook->loginFinish()
#1 DOCROOT/wp-content/plugins/facebook-publish/lib/class/hybridauth/Hybrid/Endpoint.php(229): Hybrid_Endpoint::processAuthDone()
#2 DOCROOT/wp-content/plugins/facebook-publish/lib/class/hybridauth/index.php(43): Hybrid_Endpoint::process()
#3 {main}
Next exception 'Exception' with message 'Authentication failed! Facebook returned an invalid user id.' in /DOCROOT/wp-content/plugins/facebook-publish/lib/class/hybridauth/Hybrid/Auth.php:439
Stack trace:
#0 DOCROOT/… in DOCROOT/wp-content/plugins/facebook-publish/lib/class/hybridauth/Hybrid/Auth.php on line 439
Server is running PHP 5.3.10
