When The Monkees sneak Vanessa out of the house to tutor her, she's wearing a sweater and jeans, and her hair is in two ponytails. In the next shot they are at the beach and her hair is all wet from the water. Then in the next shot she's back in the sweater, jeans, and two ponytails, with no sign of her hair having been wet.
The Monkees' hair is noticeably longer during closeups of the performance of their songs, as these sequences were re-shot a year after this pilot was filmed.
In the "Hamilton" skit which The Monkees act out, Aaron Burr declares that Alexander Hamilton has publicly accused him of treason. Noone made such an accusation against Burr until 1807, three years after the death of Hamilton.