The main thing that a new investigation could do is re-examine the JFK's body, to see if the any evidence of the bullet movements of the "magic" bullet and to confirm the impact location of the head shot.
Unfortunately the other things I would like to get solved will now never be solved, the people are dead or too old to be of any real assistance
Getting the full testimony of the 4 ladies on 4th floor is now too late. Garner to confirm actions of Adams and Styles and her own, Dormann to confirm movements of the other three.
Sorting out Hines and Reid failure to cross paths (one of their testimonies just doesn't fit the other).