Some sites have review audits, and some don't. Which ones currently do and what is the criteria for activating this feature?
currently they are active on Stack Overflow, Super User, Programmers and Server Fault. – Rory Mar 29 '13 at 12:34 [emphasis added; note the timestamp is a year old.]
This answer-in-a-comment seems to omit Mathematics, as per the comment you linked, and Ubuntu according to @Thisismuchhealthier. (Thanks!)
Please feel free to edit in any others as they arise, or comment with some kind of supportive link, and I'll edit it in myself.
Can't speak to the criteria for implementation, but I'm guessing this is decided internally on a per-site basis, maybe sometimes spurred on by feature requests from users (e.g., Drupal has one going).