I wouldn't double the thread, that make cause it to show. I bury my knots on the inside part of the binding you sew over so they don't show. Also keep you stitches close together. Anything more than 1/4 inch can get "gappy" and I think you get counted off for that too. Basically you want a smooth finish with invisible stitches, uniform width of the binding and a pleasing fullness, not flat like there's nothing inside the binding, or too fat like there's too much batting and fabric. You don't want the binding to look like it's straining to wrap around the back. If you do the french fold binding pay extra attention to turning the corners so you have a perfect miter with no stitches showing. I can't remember if they get picky about how you finish it where the ends of the binding meet.
Note: Duhhhh...it's been too long of a day. I got this confused with the quilt show thread :) I am going home now, my brain left 2 hours ago :)