If I were hiring a Product Owner I would ask her one question:
How would you build Facebook if you were a Facebook (Twitter, Instagram, Pinterest, LinkedIn, any other well-known product) Product Owner?
And I think this is a very good theme for a whole interview, starting with an idea and then discussing all other important topics:
- Who is the main customer
- What are the top features for the backlog
- What team would be needed, what skills
- What infrastructure will be needed for the product
- How much investments do we need to start
- What are possible monetization schemes
- How fast may we expect profit
- What loads may we expect
- How will we grow this product
I think these are all very important questions for Product Owner to answer, even for existing ones and existing products. I came up with this today while reading http://thenextweb.com/dd/2013/12/02/much-cost-build-worlds-hottest-startups/.