The documentation says about private_info:
access full history of a user's private actions on the site.
What this means right now (API 2.1) is that that scope is needed to use the /reputation-history/ paths:
Discussion (of
/users/{id}/reputation-history/full)
Returns a user's full reputation history, including private events.
This method requires an access_token, with a scope containing "private_info".
This method returns a list of reputation_history.
According to the docs, at least, no other paths require that scope.
