Automatic Speech Recognition (ASR) has transformed daily tasks ranging from video captioning to medical note-taking. ASR systems' growing use warrants robust and standardized auditing approaches to ensure automated transcriptions of high and equitable quality. We identify three pitfalls in existing standard ASR auditing procedures, and demonstrate how addressing them impacts audit results via a case study focused on patients with a language disorder, aphasia. First, audits often adhere to a single method of text standardization during data pre-processing, which (a) masks variability in ASR performance from applying different standardization methods, and (b) may not be consistent with how users -- especially those from marginalized speech communities -- would want their transcriptions to be standardized. Second, audits often display high-level demographic findings without further considering performance disparities among (a) more nuanced demographic subgroups, and (b) relevant covariates capturing acoustic information from the input audio. Third, audits often rely on a single gold-standard metric -- the Word Error Rate -- which does not fully capture the extent of errors arising from generative AI models, such as transcription hallucinations. We propose a more holistic auditing framework that accounts for these three pitfalls, exemplify its results in our case study, and propose a path forward for implementing robust ASR auditing practices -- with a particular focus on medical applications.