Generally, as a Product Manager you need to come across as confident. Your ability to influence others will often depend on it. It won't matter if you bring solid data and years of experience with you. If you're hesitant or come across unsure, your day will be much much harder.
Confidence is great, but don't confuse it for Hubris. Product Managers need to know when they're wrong, admit it, understand it, and learn from it.
Mumbling, or a poor grasp of the language your company operates in, is a major red flag for me during the hiring process. Any hint of a communication problem will compound when they join your company. This extends past just being able to speak clearly, of course. Their ability to communicate ideas visually, like a feature mockup or a plan for a flow of work are also critical.
Can they come up with creative solutions, ideally using new or recent technology, to solve real problems. In my experience, asking the candidate to go through a product challenge is a great way to test for this. For more on this, see how to create a great product challenge.
I don't see how in this day and age you can't be at least reasonably technical when it comes to Product Management. To not now what an API is, or what is possible with them, will massively hold a Product Manager back. I always prefer Product Managers who come from a development background, or perhaps learned how to code themselves because they had an idea they wanted to bring to life. For more, see how to test product mangers for technical ability.