I agree, the flap about the medals goes to the character issue, but aren't crucial. His activities after he returned however deserve full scrutiny:
His meeting with the enemy in paris while still a member of the naval reserve
his attendance at a meeting in kansas where the assasination of 6 senators was discussed- he voted against it, but remained a member of the group for months after and did not report it to any authority- this info is taken from fbi files and is not conjecture
His groups making of audiotapes that were played in hanoi prisoner camps to break the will of the prisoners