Leave the old fill compound in the holes. What I do with the 16" on center problem is by cutting out a piece of 1x4 pine to 20"(for the 18" rod) or 26" (for the 24" rod)and knock the sharp edges off with a 45 degree angle all the way around the piece of wood. Prime, paint, screw and glue (construction adhesive)the piece of wood into the studs (which are the 16" on center) and attach the towel rod to the piece of finished wood. Does this make sense? You will never have to worry about the towel rod being ripped out of the wall because the wood will be screwed into the studs and glued onto the wall.