The dark side of me likes the theory proposed, and quickly disappeared, that Kennedy was shot by mistake by Oswald. He was after Connally for some veterans bennie grievances.
The real cover up is that the Powers That Be decided to make JFK a martyr rather than some poor schlub who was accidentally killed by a lousy marksman.
That would account for one odd thing. When the rifle was tested it was not sighted in correctly. I always just guessed it was knocked off by rough handling or maybe somebody playing with the scope adjustments etc.