i am a professional drywall hanger and finisher. The best way to repair the holes is to get a piece of drywall, if the hole is 1" cut a square of drywall 4"x4", from the backside in the center cut a circle the same size as the hole, cut 4 or 5 lines from the cut to the edge of the drywall. So it will look something like this on the backside
then carefully break off the outside pieces peeling them away from the front paper, leaving the face of the drywall paper intact and square. put mud on the backside of the plug piece, insert it into the hole, pull your mud blade across it pushing the mud out to the edges leaving it completely smooth. Cover it with a coat or 2 of mud, sand if needed and it's patched.