How would you improve your favorite product?

A PM can only make improvements to a product if he is intimately familiar with that company’s vision and product strategy. So this question only tests someone’s ability to bull$h^t with confidence. You really want a product manager who asks the right questions and validates assumptions — so this trait runs counter to what you need. But a good variation on this question would be to ask the candidate about the product that they built and how they would improve it.