1. Follow instructions. People often have specifications about whether to attach or copy & paste your resume, what to put in the subject line, whether to include a cover letter, etc. If they say NO CALLS, don't call.
2. Pay attention. See if you can find out what company it's for. Tailor your letter to the job - if it's for an agency, don't write about how you can't wait to work in production. Same thing with "objective" on your resume - I actually think you can trash this section. But if you really want to have one, make sure it doesn't say "to get a job in development" when you're applying for a job at a management company or something. Don't go on and on about your writing and directing accomplishments if the job does not involve writing and directing. And if the posting says "send resumes to Sally Brown," don't address your email "Dear Sir or Madam" or "To Whom it May Concern." It concerns Sally Brown.
3. Don't make your resume more than a page long. Use smaller fonts and wider margins if you need to - but when you're applying for entry-level or nearly entry-level jobs, it's ridiculous to go onto a second page.
4. If you're not already in LA, you need to specify that. You probably shouldn't even be applying yet at all. There are sooo many people already here - the employers aren't going to wait for you.
5. Keep your cover letter short - and for Hollywood, I'd err on the side of not being super formal. Try to let a little bit of your personality show through rather than sounding like your letter was automatically generated from a Career Services website.
6. Check and double-check for grammar and spelling mistakes. Duh.