During Claude's bus trip at the start of the film, he passes a field of ripe orange pumpkins, indicating that the time of year is autumn. When he gets to New York, specifically after the party where George stops the car, yellow forsythia are in bloom indicating that the time of year is spring, and the trees are all green instead of autumn colors.
When Berger enters the camp in the borrowed car wearing the borrowed uniform, just before the barrier is raised by the MP soldier, Berger wears sunglasses, then a shot from the side shows him in the car rolling through the gate without glasses, then the next shot shows him front again with the glasses on again.
During the "Good Morning Starshine" scene in the convertible the mirror in the middle is removed (you see only a dot) to get a better shot at Sheila, who is sitting in the middle. Later when Berger drives to the army camp the mirror is back where it belongs.
When Berger starts his dance on the table at Sheila and Steve's engagement party, Hud is turned towards Sheila's end of the table and smiles at someone. He doesn't have a cord in his hair. Then there is a cut: he is looking towards the near end of the table and he has his hair cord back. Then he doesn't have his cord ....
The goof item below may give away important plot points.
Incorrectly regarded as goofs
When Berger goes to Vietnam the army only knows him as Claude Bukowski, but on his tombstone it has Berger's real name. However, at the beginning of the movie Berger is burning his draft card. It is possible that he could have told someone of the mistake, and, since Berger was supposed to be drafted anyway, they kept him.