All SFC settings are stored in one option. So uninstalling through WordPress (deactivate, then use the uninstall link on the Plugins menu) should remove its settings just fine.
But honestly, uninstalling and reinstalling won't fix anything. You need to identify the problem and correct it. Usually the problem is as simple as correcting the Site URL on the Facebook App Settings page. Just go to http://www.facebook.com/developers/apps.php and edit the settings, pick the website tab, and make sure your URL is correct. Caps matters. Lack of www or not matters. The URL must be *exactly* what shows up in a web browser when viewing your site (and have a / on the end of it).