Leaving the old felt does not effect the new roof, except for the warranty issues. It is good practice to remove the felt to inspect the deck. Without removing the felt there is no way to tell if there are defects, rot, ect.
The improper nailing is a much bigger concert. Are the nails above or below the nail strip?. High nailing can lead too a lot of problems down the road. Do you have any picture?
I would recommend doing some more investigation. If you can safely do so, check the nailing in a few different areas to see if it is a wide spread problem and go from there. Owens Corning in particular makes it pretty straight forward as to where the nails being.