The pristine bullet that was recovered from the stretcher which is part of Arlen Spector's "single bullet theory" certainly didn't fragment. None of JFK's wounds other then the head wound show anything like that kind of damage.
There are many things from the books I've read on the topic that give me room for doubt among them the parade route being changed on the morning of the motorcade, the fact that only the three shell casings were found in the 'sniper's nest' and no more rounds were found among Oswald's possessions at his room or at Marina's home. If he was going to attempt to do something like that I would think he might bring some extra ammo.
That they interrogated him for 12 hours and there is no transcript. That a hoodlum with known underworld ties murdered him. I saw it live on TV that morning. That JFK's autopsy was botched and the brain of the President of the United States along with tissue samples is missing. I am not an expert on autopsy by any stretch but I would think the bullet fragments in the brain could have told us something that might have been conclusive.
In 1979 the House Committee on Assassinations concluded that both President Kennedy's and Dr. Martin Luther King's assassinations had been the result of a conspiracy BTW.