From the Washington Post Article:
In September 2002, the younger Gore was ticketed for driving under the influence. He was pulled over and ticketed by military police just outside Fort Myer in suburban Virginia, but was not taken into custody.
In the summer of 2000, Gore was cited by the North Carolina Highway Patrol for driving 97 mph in a 55-mph zone. Under an agreement with prosecutors, a reckless driving charge was dropped in the North Carolina case, but he was fined $125 for speeding and his driving privileges in the state were suspended.