One of the things I've looked at is whether or not there are any errors on the resume or cover letter. No spelling
errors or grammatical errors.
I've also been very unimpressed by resumes with things lined out and written in ink. Back in the day before PC's when resumes had to be taken to a printer and you paid for 50 copies or so that might have been acceptable, but not today when it takes very little time to change an address or phone number before printing the resume.
Know enough about the place you're applying to and the job you're applying for to show in your cover letter why you'd be a good fit.
One thing that can be difficult is to promote yourself without sounding arrogant. Have a couple of people who will be honest with you to read the letter.
Clinical experience: I wouldn't put too much of that in. You don't want to "pad" your resume. Of course, if you voluntarily did extra clinical time or an internship or whatever in a particular area, that would be worth including, especially if it's applicable to where you work now. The usual nursing school clinical experiences can be assumed by the person reading the resume.
I'd go ahead and include the EMT and paramedic experience. Just be prepared, in an interview, to explain how you think that helps you in the area you're interviewing for. That would be pretty obvious in ER, but not so much in an area like surgery or med-surg, so think that through and be ready to explain (I've learned to react calmly in a crisis, I have started many IV's and am adept at that, etc. etc.)
Hope this helps!