To shut off all comments/trackbacks/pingbacks in the WordPress Admin, the steps for cleanup are:
- remove all pending comments marked as spam (the WP Optimize plugin is great for this)
- disable all comments/trackbacks/pingbacks in the WP Admin (following all the steps here: http://premium.wpmudev.org/blog/wordpress-comments-off/)
- remove all Theme references to
comments_template/pingback_urlin the active Theme - set archive posts/etc. to disable comments/trackbacks in the database: http://codex.wordpress.org/Combating_Comment_Spam/FAQ#I_have_disabled_comments.2C_but_comments_continue_to_be_posted
- [OPTIONAL] add Theme code to disable comments and access to comments: http://www.dfactory.eu/wordpress-how-to/turn-off-disable-comments/
- Deactive/remove antispam plugins after all steps are completed above. No plugins should be needed if you followed the steps above, but if you need to install a free plugin, Antispam Bee is a good choice
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.