To shut off all comments/trackbacks/pingbacks in the WordPress Admin, the steps for cleanup are:
pingback_urlin the active Theme
All this might seem like overkill, but comments et. al. can be a backdoor to spam and malware. I'd rather take 30 minutes to shut this down on our sites where we don't use these features than have to restore from a hack/attack.
Now, do we want to leave [archive] WP/Facebook comments on sites where we've had active discussions? I think there's benefit from users seeing activity on sites if there was some in the past. If you're keeping them, be sure not to remove the appropriate comment code from the Theme that actually displays the comments.