If you really want to get into management consulting the easy path is typically to toss out all the value words and feelings you may have about the people involved. Don't even think words like "loathed", "ineffective", "parroting" etc. Instead you go to the hard facts. What is the properties of the department? How does it compare to other similar departments? Do they have procedures and routines? What are they? Do they have qualifications in relevant fields? etc. Don't fall in the trap of trying to pin everything on a single person, as this kind of situation is typically part of the culture of the department. The head of the department is a symptom, not the single cause of it all.
Also remember, that those that hired you are probably also responsible for hiring that head of department. Calling him incompetent is roughly the same thing as calling the people who hired him incompetent. Not a good way to build professional relationships or helping people.