When Rory is talking to Christopher, the window to his right is open in some shots and closed in others.
On the phone with Emily, Lorelai tells her on her 13th birthday she went to the movies with Richard and the films they saw were "Grease" and "An Unmarried Woman". It was previously established in the original series that Lorelai was born in 1968. Both movies were released in 1978 so that would imply that Lorelai was born in 1965.
Luke & Lorelai were to get married on November 5th, 2016. A full moon is clearly shown. However, that date was still a week from the full moon.