I would totally respect a nanny who was discerning enough to ask questions about my parenting style, most important needs, etc... - a la the list from 14:43 - which is great.
As a mom, I'd also love a nanny who is interested in the kids. What are they like? Is there anything important that I (the prospective nanny) should know about little Johnny or little Dora?
Obviously the questions would vary based on the age of the kids also. For infants you'd want to ask questions about feeding/napping schedules (which would give you an important read on the parenting approach and/or knowledge). You might also ask if there are things that they (prospective employers) are specifically looking for, would like the nanny to help them with, etc...
And maybe just "what kind of nanny will be the best fit for your family?" would get you good info.
Good luck! Just the fact that you're asking for this kind of advice makes me think you'll do great in an interview.
FYI, one nanny I rejected almost immediately, who appeared fantastic on paper, came into my house and started correcting how I had things set-up, "Oh, we'll have to change this." kind of thing. Her interview was short. The nanny who asked me how I wanted her to fold/categorize the babies' clothes was hired.

(Not because she was worrying about their laundry per se, but because she was interested in what worked for me, what my system was, etc... rather than trying to prove her knowledge by correcting me.)