Interesting post, Madfox. Not sure all the questions will be relevant to all occasions - one of the reasons I hate checklists - as soon as you get a No you are forced into a decision that may not be the right one.
I don't work for an "alphabet soup" registrar, so I'm not bringing a dog to this fight.
But, I've been there, done that, so here's my $.02. And before Acme, Inc. signs with someone because some smooth talking, well-dressed hombre shows up, here's what to ask before you enter admin/scheduling ****!
a) Is the registrar TS-approved?
(Love 'em or hate 'em, they only allowed a third of CB's entry, thank you!)
Again you have to understand the assessment criteria - and with TS it was volume - full stop. The accreditation body wanted to restrict the number of CBs they had to accredit - and they did so by looking at who was doing the most business - hardly the best quality recommendation.

But hey we're only talking about a quality standard here and I'm going over old ground covered in other threads ....
b) Do you have local auditors?
Good question. Again if you're interested in costs local is better and communications may be a lot easier - no guarantee of quality.
At the last company I worked as QM for we had an auditor who lived less than a mile away and he was a laughing stock with the company.
Ah well!
c) If not, can I cap travel costs? (And if not, do I pay for "travel time?")
Again important to keep the costs in check but no indicator for quality of service.
Think about the amount of time you can spend dealing with nonconformities that give no benefit to your company - just to satisfy an auditor who won't listen to reason. I would much rather pay a flight cost and get someone who understands my business.
d) "How long have YOU been with ABC Registrar?"
Is this for the salesman or the auditor - either way it doesn't tell you much. If the CB is growing they have to take on full time / contract staff. A certain amount of "churn" is good it helps bring in new ideas and gets rid of stale ones.
"Are YOU a Lead Auditor?"
Be careful with this question - if this is for your auditor they may not need to be, particularly if you are already registered. Also all lead auditors have to go through a qualification process to be approved - if the auditor is good enough keep hold of them - even if they don't carry a card.
Some CBs (like mine) don't insist on a card carrying lead provided they meet the criteria of training, experience of industry and of leading audits. For example I was certified from 1991 to 2000 (ish) and then went into industry as A QM so had to let it lapse as I wasn'ty doing enough qualifying audits. To get back in I had to go through the whole qualification process again - I don't think so!
e) Can I interview your auditors?
Again a good question - and probably the best indicator of how the audit process is likely to go. I recommend this one wholeheartedly. A word of warning - if you want an efficient CB you may not get to see the auditor face to face, otherwise they have to build this cost into your fees.
f) Can I have the same auditor for three years?
I don't think you will get any CB to guarantee you this. Most try to give continuity but with growth, churn stc. you do get change.
g) What's your annual "cert fee?"
You should have a good idea of prices throughout and can even ask for a quote for the three year cycle of certification. Some CBs will guarantee prices (but they build in an uplift each year).
h) (Sshhh, don't ask the rep...call on your own and see what kind of response you get to an inquiry. One "alphabet soup" registrar I know has a mean response time of 4 weeks, for quotes!! Ask a technical question, like their interpretation of the standard. If you get hemming and hawing, move on!)
Again a great idea. This gives you a good insight into responsiveness. Bear in mind some of the larger CBs will have more complicated communications - do take this into account but pursue it to see calls get returned.
i) References (locally), please.
Ideally references with the same auditor - you can get great references from another industry sector and it is only your person that gives companies a hard time!
In the U.S. I recommend medium-size shops. I found out that, after signing, the Big Kids just threw my clients into the bait bucket with their other catches!
Yes, big enough to matter, small enough to care. Not all big CBs lose the personal touch but a lot do.
Although when the company is big enough themselves the larger CB assigns them a major account manager!