At the very least, health checks determine if the project is complying with standards and procedures including the project methodology. They can also compare projects to 'best practice' or 'common practice' and look for common problems.
Health checks need to be done by people who are conversant with current project management techniques. Their experience will be essential in recognising common problems and working within standard methodologies. We suggest using staff from your project office, or specialist consultants such as Island Consulting.