complement/compliment: To compliment is to make a flattering statement. To complement is to go well together. A casting director might compliment you on your professionalism. You might tell her that you think you'd be a great complement to the ensemble cast of the comedy she's working on.
principal/principle: You are auditioning for a principal role, not a principle role. "Principle" is never an adjective; it is only a noun, usually meaning "a rule or code of conduct." A movie that has good principals might be an awards-season favorite, whereas a movie with good principles will probably never make it out of development.
fleshed out/flushed out: To flesh out is to expand, improve, give more substance to. You work with a director to flesh out your role. You flush out when you get a corrosive substance in your eyes.
everyone/every one: You would like to thank everyone at GO Casting for their time. You hope every one of your spec scripts gets picked up.
onto/on to: This mistake is so common that, to be honest, even if you make it, it will probably go unnoticed. Here is a good shortcut: If you can insert the word "up" into the sentence before "on" and the sentence still makes sense, then "onto" is probably correct. If not, "on to" is likely correct. The mistake occurs most often with "hold on to." It's not "hold onto."
The English language being what it is, there are a ton more pitfalls like the above, but a little knowledge goes a long way. It doesn't hurt to have a reference like the AP Stylebook or Chicago Manual of Style on your bookshelf. At the very least, have a syntax-savvy friend look over your letters before you send them. The grammar-conscious are everywhere, in all walks of life, not just in classrooms and newsrooms. Why risk losing a job over something so easily correctable? After all, isn't meticulous attention to detail what separates the great actors from everyone else?