Manual:Removing embarrassment

Certainly, people can post bad things onto a wiki, a message board, or a mailing list. Yes they didn't heed the warning, didn't follow the rules. Didn't ... anyway yes, we have of course edited out the words in question, but there they still are, still accessible in old revisions and RecentChanges. How can we clean up such embarrassing matter from our MediaWiki installation?

Cleaning up embarrassing words in an old revision
You can delete the page inside the wiki interface, and then undelete all revisions except the problematic one. Then only sysops can see it. If that's not enough, and you don't want to install Extension:Oversight, edit the database. Again, this is what was done on Wikimedia before Oversight existed.

Also the maintenance/deleteOldRevisions.php maintenance script can mass-delete all old revisions of pages and their associated text records.

Cleaning up an IP address

 * A beloved user on my wiki has mistakenly edited while not logged in, leaving his company's IP address in the history of A_Sensitive_Article and RecentChanges, etc. He is begging me to expunge his IP... What is the best way?

Manually edit the database. Edit the revision metadata in the revision table. That's basically what sysadmins do on Wikimedia when such a request arises, that can't be handled through Extension:Oversight.