Do not make a private complaint more public than the solution requires.

Where you raise a complaint decides what it turns into. Said privately, it is a problem to be solved, and said in front of an audience, it becomes a position both people must now defend, with retreat made expensive. Publicity is sometimes necessary once private routes have failed. As an opening move it usually costs you the cooperation you needed.

Take the issue to the person, then to whoever can fix it, and widen it only if neither works. Ask yourself honestly what the extra audience is for.