Brian tries to get another man to buy him a beer, saying that he is not old enough to do so. The drinking age in Illinois in 1962 was 18 and Brian would have to be at least that to enlist in the military then.
Playing over the scene with the graphic "Loyola University, 1964" is The Byrds' version of the Bob Dylan song "The Times They Are A-Changin'" which was not recorded until September, 1965. Dylan's version was released in January, 1964.
At the end during the BBQ, the mother asked "How's my boy today?" there is a boom mic visible.