Authenticity Mavens (also known as Period Police, Garb Nazis, etc.) is an SCA term for someone who is overly (some would say unfairly) critical of another's clothing, particularly the finer details of historical accuracy.
These terms are insults and are generally not applied to those who are merely attempting to do things accurately; rather they are used to refer to anyone who is perceived to be trying to force their standards of accuracy on others, particularly beginners who have yet to embrace the full rigors of historical recreation.
As a caution, someone who gets the reputation as being overly critical of other people's accuracy may find themselves shunned except by those with extreme confidence in their own standard of recreation.
In the SCA
The broad historical sweep of the Society and the generally flexible approach to historical accuracy tends to make inaccuracies somewhat more excusable than in stricter recreation groups, but this also widens the scope for some truly egregious historical inaccuracies in garb.
There is widespread fear of Authenticity Mavens, by whatever name, in the SCA, particularly among newcomers. However, as one of the basic ideals of the Society is courtesy, these people are far less common than Dame Rumour makes them out to be.
Generally, the best approach to a glaring inaccuracy is a courteous (and private!) explanation to the offender of what is wrong. Frankly, though, if one is going to stress about minor offenses, the SCA may not be the best place to indulge one's passion for re-creation.
In Re-Enactment Groups
As the minimum standards of reenactment groups are considerably higher than those of the SCA, one might expect a larger number of Authenticity Mavens but the opposite is in fact true, as there is a better general understanding of what is considered acceptable.
They are, however, common in some UK re-enactment groups, where they constantly patrol seeking to ratchet up the authenticity standards to ever higher levels, and loudly criticizing anyone who, in their opinion, does not come up to the "correct" standard.