I love the "best advise my instructor gave me..." so much that I'd like to see what the instructors out there would like to share with those students who are reading.
When I teach others, there are a few pieces of advise that I like to share with my students. Each piece depending on what we are working on at the time.
Forms: Look before you throw that technique! Make the judges believe that you are actually fending off attackers!
Basics (kicks, punches, etc.): Pivot! Chamber!
Sparring: Watch the eyes. Most will give away where they are going to strike with their eyes. I do it, you do it. Learn to keep your eyes on theirs.