Once you have finished and are sure it is perfect, put it in a drawer for a day or two and then take a fresh look. Then have two or three other people look it over as well. Of course, check for grammar, spelling, and punctuation, but also look carefully for formatting. Be sure that headings are in the same type of font. If you bold print one date, bold print them all. Check for random indentations and auto-corrected errors, especially incorrect capital letters after periods following abbreviations. It seems like such a little thing, but you want to prove you are someone who pays attention to detail. You won’t get a second chance if your resume has careless errors.
I just wanted to say I agree wholeheartedly about following up if you don’t get a response (and you’re serious about the professor and/or line of work).
I wrote to a professor enquiring about full time openings in her lab but she didn’t reply. I followed up after 2 weeks, and she replied almost 2 seconds later apologizing for not getting in touch sooner because she was out sick and the email then got forgotten.
In this case, there was a happy ending. The prof flew me out for an interview, and I’m still at the same lab working full time.
I was never more glad of my persistent stick-to-it-ness.