9:58 here. I'll start by suggesting this list from Aupairmom.com:
http://aupairmom.com/interviewing-au-pair-candidates-every-question-youve-ever-recommended-we-ask/2010/03/23/celiaharquail/
Read the comments too - there are some very wise host parents who post great suggestions.
My philosophy is that I need to find a mature and responsible young adult who takes good care of kids and who likes kids. Then the AP has to understand that I have some "bright line don't do's" - they would be cause either for involvement of the LCC or immediate rematch. There are very few of those, other than obvious safety concerns. Then the AP needs to be someone I would like living with. And last but not least, we need an excellent driver.
I like a lot of the questions from AP Mom because you can get a sense of why the AP is coming to the US, does she like kids, can she handle a long (but no more than 10 hour) day with kids by herself, how would she handle disagreements between the children, what is her philosophy on discipline, is she a self-starter, etc. Some of the questions are good for sussing out how adventurous she is and if she'd weather homesickness and culture shock well.
Ask open-ended questions about what she does in her spare time, what does she like to do with friends, what did she do last weekend. You want to get a sense for her real personality and how she like to spend time rather than the "idealized version" that a lot of people like to present in an interview (which is human nature).
You should decide what you absolutely will not tolerate. Some of this you won't know until after you've had an au pair. My list includes smoking, phoning or texting while caring for children or while driving, and posting photos of the children on social media. Be careful with the smoking issue, if it's important for you to have a non-smoker. I've not had a problem with ProAupair APs, but it's been a problem in the past. Social smoking is common, and someone may indicate "nonsmoker" yet that may be far from the truth. We are explicit about how smoking is a problem, and it's a cause for rematch. If someone comes in from a night on the town with a vague hint of cigarette odor on her clothes, I'm not going to have a big problem. If the AP smells like cigarettes often, or if our AP car starts to smell like cigarettes, that's a problem.
Regarding driving: we look for au pairs who have been driving several years. I ask about accidents and tickets. I ask if she has a car, does she drive city roads, country roads, highways, does she drive stick/manual, is she comfortable driving in city traffic, how many kilometers per week does she drive, does she feel comfortable driving in the nearest major city (like Munich or Berlin), does she commute by car to work or school, has she ever taken a road trip, what's the longest road trip she's ever driven, etc.
Beyond that, I would just have a conversation with her on skype and see if you click. Have multiple conversations, and if you have a DH / partner, involve him/her too. If you live with someone a year or more, you definitely want to click. Good luck!