Here are some we recently asked (in no particular order):
• How would you work through situations where our product visions differ?
• There will be a ton of ambiguity in this role, basically building a product org from the ground up. How do you feel about that & what would you tackle first?
• Tell me about a time you had to deliver bad news to someone in a professional setting.
• Lots of people say you shouldn’t hire externally for your first product person, rather build them up internally to optimize for trust, culture, fit, etc. Thoughts?
• If you were me interviewing you, what is another question you’d definitely ask?
You may also want to go deep into the product manager’s knowledge of the industry, competing products, pricing etc. You can pick one of the products in the market and ask him/her to create a roadmap for a year, go into depth of the thought process behind that. You can also go into depth of your product and ask him/her to present back to you on specific things you are working on. Previous experience in building and managing PM teams would be a great plus.