It depends a lot on factors like what industry are you in and what phase your company is in. Off the top of my head, here are some thought-starters:
1) What products and services are you are passionate about and why?
Good: They will get excited - and tell you about design, customer experience, price, performance of how the product or service works, the operational design (how it is built), how it gets to customers, how it gets sold, and how it is branded/ marketed.
Bad: XYZ product, because they look cool
2) Tell me how you resolved a conflict between people.
Product Management is about leading people as well as the product.
3) How many years experience in software development (or some other area for different industries) do you have and what did you accomplish?
4) How many years of customer research experience do you have and what did you accomplish?
5) What do you do to uncover customer needs?
Good: They look for customer needs and why they are needed in context of the customer's life, sometimes unspoken - also track macro trends and what the future will look like
Bad: Ask the customers to provide feature requests
6) How does the job change as your product grows?
7) How do yo balance incremental product improvements with game-changing improvements?
8) How do you prioritize features?
Good: Based on roadmap/ vision validated by what you know from customers, trends, etc.
Bad: First-in, first out based on feature requests
9) How do you know which customer requests to ignore?
10) Tell me why you do research. What to you want to discover?
11) How do your competitors impact your feature planning?
Good: Good to be aware, but we set our own vision
Bad: We create a comparative feature grid and match it
12) How do you collaborate with the people building the product?
Good: We meet to make tradeoffs based on the future vision
Bad: I ask for features, they code the features with little context of the future