Although essential to revealing biased performance, well intentioned attempts at algorithmic auditing can have effects that may harm the very populations these measures are meant to protect. This concern is even more salient while auditing biometric systems such as facial recognition, where the data is sensitive and the technology is often used in ethically questionable manners. We demonstrate a set of five ethical concerns in the particular case of auditing commercial facial processing technology, highlighting additional design considerations and ethical tensions the auditor needs to be aware of so as not exacerbate or complement the harms propagated by the audited system. We go further to provide tangible illustrations of these concerns, and conclude by reflecting on what these concerns mean for the role of the algorithmic audit and the fundamental product limitations they reveal.