You can check to see if the end of the taper is bottoming out in the ferrule of the point.
With my Tru-taper tool, this sometimes happens, depending on which broadhead I am using.
Also, as a wooden shaft is not perfectly round, the back edge of the taper sometimes is cut further down one side of the shaft than the other.
If your points are spinning true, with no major run out/wobble, this isn't going to cause you any major concerns.
Touch up the finish, where it has been cut off, and do the same with the scratches.
Good luck with your arrow making!
R.W.