The article discusses some questions to ask including:
Is this right for me?(Read the full text of "Is Paying for 'Concierge' Health Care Worth It?")
Will you take my insurance?
What happens if I get sick while I'm out of town, or while you're on vacation?
Do you make house calls?
How will you handle my medical records?
What if I change my mind or don't like the service?
Beware that some states (like Oregon) are trying to restrict this practice model, by requiring these doctors to register their practices with the state's insurance department on the grounds that they're accepting fees for the promise of future medical care.
(WSJ link via Dr. Art Fougner.)