Make your research plan, in particular, accessible to any reasonably good mathematician. Accessible to outsiders and yet it penetrates deeply into the subject. In general you should not bullshit nor pad your application. It hurts you, as faculty are very experienced at reading through bs. It is very difficult to write well.
Few people manage to do it.
In fact few experienced professors manage to do it, despite years of experience. Ask them to be very critical and very hard on you. Try not to be too boastful, but also do not be too modest. At UGA we get to see a lot of job applications and it is clear that a lot of candidates hurt themselves by not spending enough time on their application. They have not thought carefully through what they are trying to achieve in their application and they have not made themselves appealing enough to us to give them a second look.