Let’s assume the goal is to hire a PM that will transform your shitty product into world class dominance and the company is not the primary limiting constraint.
A good PM will be ambitious about product quality. It’s the hill they are willing to kill their own career on. Before new features are added the existing features must work without error as widely as possible and must execute quickly. If that means going to war with the developers then so be it. Developers not willing to achieve the quality vision of the PM are a problem to be removed. Developers do not pay the bills, sales do.
Secondly, the existing features of the product needs to achieve business results superior to the competition. This may require original technology solutions, but more often than not it will require building new business partnerships, or repairing existing ones. For example e-commerce solutions require superior inventory, better incentives, and cheaper prices.
A good PM sets ambitious numeric targets. This can include sales growth, execution speed, support costs, inventory quantity, latency, headcount size, and more. A PM will not control any of this but nonetheless knows their numbers and is willing to use this evidence to destroy all internal obstruction.
A good PM is fully aware of their products current operating state. A product is never perfect and requires periodic downtime for maintenance. A good PM is willing to work with operations to establish necessary redundancies and schedules that minimize business disruptions.
There is more, but this is a start.
Walk out of another and it’s more meetings, more docs, and somehow less clarity than before.