Part of it is trusting your vet. I'd want the vet up to date on procedures, with access to a variety of anesthetic agents and knowing when to use what. Some anesthetics are better than others when there may be issues with the kidney and/or liver function. Does the vet also use local nerve blocks in addition to general anesthesia before doing any extractions? Using local in addition to general anesthesia may prevent wind-up, a type of pain response which can be difficult to manage. Ask ask for a complete description of what is to be used - IVs, general anesthetic, and local anesthetics, tools/machines/X-ray, recovery area, expected time under anesthesia, whats available for resucitation if there should be an arrest, blood pressure, etc.
Another part is the cat's current general health - stable on medical management? Evidence of kidney disease? Liver disease? Both the kidney and liver should be working fairly well; this may be assessed, at least partially, with blood tests.
And finally, what do you want done if there is a problem - if the cat has an allergic or atypical response to the anesthesia, do you want to resucitate?
The vet I use in Columbus, OH stays very current on veterinary knowledge and I've not had a problem with any of my civvies (including the seniors I've had), nor the 1 diabetic I currently have, in having a dental performed.
Observation - wow, is he ever on a lot of insulin. I searched your posts, but didn't see whether he'd ever been evaluated for insulin auto antibodies, or for acromegaly. I may've missed it, but if not, that may be something to investigate after the dental.