The president and the vice president of the United States do not fly on the same plane, even when they are going to the same destination.
In the 1976 scenes, Stone claims he wants to enter the European Union. The European Union as it is now didn't exist until 1993 - Stone would have been thinking of the European Community.
The beginning of the movie takes place in 1960, Stone is six years old and David is about three months old. Ten years later, Stone is suddenly 21 and David is 16 (according to the credits). In reality, Stone should be 16 and David should be 10. Unless Stone aged an extra five years and David aged an extra six, which is unlikely, their ages do not match up.
The President and the Vice President cannot be out of the country at the same time.
In an early part of the film which is supposed to take place in 1970, Stone and others are shown playing paint ball to determine graduation honors, when the first game of paint ball was not actually played until ten years later.