What are the registrar’s qualifications requirements for auditors? (for hiring or using an auditor) Are the auditors trained and certified under ISO 10011 (guidelines for auditing quality systems)?
How many organizations has the typical auditor certified? (Audits per year)
How many assessors does the registrar have?
What is the turnover rate for assessors in the registrar’s company? If there is high turnover that will affect the consistency of the assessment service they provide.
How are auditor substitutions handled?
Does the company provide training for auditors and other personnel to keep them abreast of developments in their specific discipline? Are there training records? Frequency of training?
Will he/she/they (auditor[s]) be available for an interview for your company to assess their suitability? (I doubt you will really want to do this, but many big companies do this.)