Every SharePoint deployment needs clear leadership and accountability in order to be "successful". Success is a loose term with SharePoint, but I like to define it as follows: A state in which the SharePoint deployment has continued to provide tangible business value over a long period of time, with minimal cost and maximum corporate adoption.
There are a lot of obstacles that hinder achieving this status of "success". Obstacles like ballooning cost, lack of compelling features, and lack of company adoption. You may start off with a bang, but find it harder and harder to keep the momentum up as time goes by. I've seen this so called stagnation in few companies, and I've really come to appreciate the role of Product Manger because of it. I've seen some companies that spin up a SharePoint site, and almost haphazardly put it on cruise control and expect great things to happen. The problem with this is that if it isn't someone's job to make things happen, nothing will happen and your initial "momentum" will come to a halt. Now, before you think I'm trying to make a sweeping statement here, even if you have a great Product Manager but don't have a budget, or executive by-in, you're going to have a hard time. However, there's a lot this person can and should be doing.
I love this quote from usabilitycounts.com, "Don't gather requirements, drive them". This driving attitude is where my idea of the Pit Bull comes from. SharePoint doesn't have an auto-pilot button, it needs leadership. I've come to see, however, that this isn't just any kind of leadership. It doesn't mean be a jerk – that wouldn't get you anything. It does however mean firmness, confidence, excitement, and a "go get it" personality. Think about the main responsibilities of a SharePoint Product Manager (not exhaustive):
- Develop Product Roadmap – aka Business Requirements
- Sell the roadmap to stakeholders, and Content Owners
- Oversee project initiatives, sign off on functional requirements, watch budgets
- Identify and train content owners, and oversee content development and enforce quality standards
You don't necessarily need to be a Pit Bull to lead in the first three areas, but the last one is what I'm here to talk about. A big responsibility for a SharePoint Product Manager is to develop and grow business leaders that can manage and lead in their respective content areas. SharePoint is a distributive technology, and is meant to be controlled and developed by its end users, not central IT. 
However, without leadership, as I already mentioned, you won't have momentum. This leadership needs to be business leadership, not just IT leadership (otherwise nobody will care – this is what will help with "corporate adoption"). So the product manager is really the leader of leaders, which makes the necessity of the position and the quality of the individual in it, especially important.
The problem is that the leaders he/she is leading aren't always motivated. This is especially true as time goes by. The Product Manager needs to "drive" these people – and this isn't so simple as "herding sheep". What makes it difficult is that most of these content owners most likely have full time jobs outside of managing and leading content development. They may not even be enthusiastic that more work was put on their plate. When dealing with people with this attitude, you need a sense of fearlessness. You need a Pit Bull. If you don't have a Pit Bull, your content development will be slow and your milestones on your roadmap will slip. Company "excitement" about a new tool will dwindle as they see a lack of progress on promised features. Also, you will have sloppy and unprofessional sites because there won't be clear accountability and training on how to make good ones. The role of product manager is similar to the neighborhood police officer in this respect. Ever see a Chihuahua serving as a police dog?
So to summarize, when you're interviewing a SharePoint Product Manager to lead your implementation, save yourself for someone that exhibits confidence, fearlessness, good communication and leadership skills, and has a strong head on their shoulders. It's a harder job than you may realize and you shouldn't settle for anything less if you value success. I would even regard these characteristics higher than possessing a SharePoint background – and the complexity of SharePoint makes that a powerful statement (save the technical expertise for a good technical lead).
No toy dogs for this job please.
Phil