OK, so after your posts I thought maybe there was an issue with the theme, but there isn't.
You can replicate the exact problem as follows:
1) Install a brand new 2.8.5 version of WordPress (I know the plugin page says only supported 2.8.4, but I doubt that's the problem).
2) Add <?php do_action('fbc_display_login_button') ?> to the comments template of the WordPress Default theme.
3) Install WP-FacebookConnect plugin (using a new Facebook application with no settings changed from default), and w3-total-cache plugin (no settings changed).
4) Visit a permalink, click Facebook Connect icon. Page reloads without being logged into Facebook.
5) Empty the page cache and see you are now logged in via facebook
6) Click the 'logout from facebook' link in the upper right, the page refreshes to still show the cached page where you are logged in.
For now I guess we'll have to go with disabling the cache when that cookie is set, but it would be nice to have this fixed for a default install at some point as WP-FacebookConnect is a very popular plugin.