I would want to know the following:
Who is his own poseik when he has a shailah?
What is his position on Medinas Yisroel?
How available is he willing to make himself to his congregants?
What does he feel are his strengths?
What types of learning programs/shiurim, lectures/yom tov specialty droshas would he initiate?
Does he have ideas for greater inclusion of the teens in shul, so they feel more involved?
And so on…