Kirk wakes up the town for a Town Meeting just after 3 in the morning. When they get to the meeting shortly thereafter, he sets of a video feed from Taylor who states that he is at his sister's house in Maine where his nephews are playing ping pong around him. Maine and Connecticut are in the same time zone so why is Taylor up at that hour - and if you chalk that up to Taylor's weirdness, why are his nephews up playing ping pong?
When Lane spins the wheel at the doggy swami stand, Paul Anka stops the wheel on the number five. When Lorelai starts reading her fortune, the wheel is completely turned around, and the fortune was taken from the number 20.
When Logan meets with Lorelai to discuss her intervening in his situation with Rory, Lorelai says she was separated from Rory for 5 months, 3 weeks and 16 days. In reality that would be 6 months, 1 week and 2 days, which is actually one week too long to be in line with the Gilmore Girls episode broadcast dates.
When Logan hands Rory the note from her mother he says Lorelai signed the seal so he wouldn't be able to read it. Rory then opens the envelope in a way that makes it clear it was never sealed.
During Luke's phone call to Anna, a tiffany style lamp with dragonflies is seen behind Anna. It is an unusual design, one that is seen in the lobby of the Dragonfly Inn. Obviously "borrowed" to fill out this scene.