Which is the most important element in writing a formal complaint letter?

A clear statement of purpose with supporting evidence. The reason being, you never want to confused the person you're addressing, because if you aren't clear, they won't really be sure of what your complaint is. And evidence of this is always necessary because though it is a complaint letter, without evidence it will be more so whining than complaining.

The complaint, you cant forget that part it is definitely the most important.