This question was posed in one of the groups I belong to on LinkedIn. I found it an excellent question and posted this response.
I am a business and personal coach. My background is in education, counseling, training and development, change management and coaching. I have helped companies and individuals in fields and areas completely outside my areas of experience. As a coach I am not an expert in your specific field (as mentioned mentors are!) I am an expert in people. Motivating, communicating, questioning, strategizing, facilitating, etc. My clients have come to me for a vast array of issues and from a variety of fields/organizations.
My point is that at least from the perspective of what to look for in a coach, it isn't their knowledge of your specific area, it is their track record of helping individuals, teams and organizations perform better. There are also different areas of coaching to consider too and what tools they are authorized to use to facilitate their coaching. What I mean here is say with a sales team I like to use the Everything DiSC Sales assessment and facilitation, someone else may use other tools.
Bottom line is if you hired a coach, mentor or other consultant what would you want them to 'fix' or improve? Then decide which discipline offers the tools to help you with your chosen area of improvement.
How would you answer this question?