In dealing with the application form itself, it helps to remember back to applying for your undergraduate degree. Neatness and accuracy still count, since you are being judged on how you present yourself. If you fill out an application by hand, make sure your writing is neat. It's also a good idea to xerox a few copies of the form, until you come up with the version you want to submit. If you have bad handwriting, typing out your answers is your best bet since you want to make sure that people in admissions can read your answers.
Regardless of how your application is written, grammar is something you have to watch out for. That's why you need to double or even triple check for typos, errors of alignment, spelling and other grammar mistakes.
Once you are done filling out the application, copy or save a version for your own records. Lastly, don't forget to include the fee. While this may sound obvious, admissions committees report that every year they come across an applicant who submits an immaculate application but forgets the fee. Don't be that person.