The scene where Madeline Albright is Rory's mother (in Rory's dream) is word-for-word the conversation Lorelai had with Rory on her 16th birthday in Rory's Birthday Parties (2000).
The recipe for Rory's signature drink (The Rory) is the same as for a flirtini (champagne, vodka, pineapple juice) with grenadine added for a pink coloring.
Alarm clock shows 4:03 AM in two scenes, first in Rory's dream, then during the night before Rory's birthday, so we can presume it is the time of day of Rory's birth.
Emily tells Logan she wanted to make sure he wasn't planning to whisk Rory off to Santorini for her birthday. In The Sisterhood of the Traveling Pants, Alexis Bledel played Lena, a girl who travels to Santorini, Greece to visit her grandparents.
While Luke is very much not into the idea of the "skit" Lorelei wants to put on where she electrocutes him and pull out his guts, Scott Patterson had a reoccurring role in Saw IV and V, one of the most violent film franchises