In most write-on competitions, writing quality is a big part of your grade. What’s more, the quality of your writing affects the perceived quality of your substance: Bad writing can keep readers from grasping your good arguments, and it can keep you from identifying your bad arguments.
So before the competition, go over any comments that you’ve gotten on your past written work, such as the papers in your first year legal writing course. Most writers make the same mistakes repeatedly. Figure out what your weaknesses are, so you can avoid them while doing the write-on.
If you can, meet with your writing instructors to see if they can elaborate on any comments they might have given you, or give you broader advice. Writing teachers like it when you come to them out of a sincere desire to improve your writing; and they often have specific suggestions that they’ll be glad to pass along.