Efficiency auditor was a title given to some of those working for the Federation Auditor General. These auditors were responsible for ensuring the efficient operation of various Federation agencies, including Starfleet.
In 2275, a team of efficiency auditors led by John Taylor was dispatched to Space Station Sigma One in order to audit the USS Enterprise while it was there. The auditors discovered issues in the ship's security department, but these complaints were later dropped. (TOS novel: Death Count)