So fun! First of all, you need to FEEL a connection to the pediatrician. Some of them are so focused on children that they pretty much ignore the parents or treat them like dirt (SOME, not all).
I actually found my doctor after I gave birth. A ped visits your baby in the hospital to make sure they're right-as-rain and to discharge them. So that's how I found my very awesome, totally chic, African-American goddess of a doctor who is young and on top of the latest medical news. I loved how she treated my baby and how she spoke to me as the PARENT, with respect. She includes me in decision-making, etc.
Ask about how their office works (when can you call with questions, will a nurse get back to me, how long is the waiting time usually, can I space out vaccinations/not have any at all, etc.).
You may also want to know how long they've been in peds (basically ask for their "track record"), their thoughts on vaccines if that's important to you, and credentials (where'd they go to school).
Mmmm, we didn't interview ours because he was my pediatrician plus others that I know. But I would ask his experience, his availability (ER calls during the night, other practitioners), what hospitals he is affiliated with. Umm sorry that's all I can think of right now.