Do a thorough style check. Take a look at the sample paper in the style book. Make sure yours looks like it. There's little stuff that you need to pay attention to, like double spacing, margins, manuscript headings, placement of page numbers. Run the spelling and grammar checkers on your word processing program.
Professors hate spelling and grammar errors.
They will reduce your grade if they find them. Some even have arbitrary guidelines about the number of errors they will allow in one paper. They can be avoided. You don't have to be an expert on grammar, or even be all that good at it, to produce papers that are grammatically acceptable. Grammar checkers on word processors will generally do a good job of catching really bad problems.