When Lorelai is introducing the movie Pretty in Pink (1986), she says "All right, girls, um, you're about to meet someone very special to me. Her name is Molly Ringwald." Lauren Graham, who plays Lorelai, actually starred with Molly Ringwald in the short-lived TV series Townies (1996) in 1996.
When Lorelai is talking with Luke in the diner after he returns from his trip, she says "Did you steal me the Constitution? Cause that could be the start to a really dumb movie." This is a reference to National Treasure (2004) where the main characters steal the Declaration of Independence, and two of the characters end up romantically involved.
Rory tells Logan that he's in the best hospital in New York City, then says that the best hospital in New York City is basically the best hospital in the country. But actually, according to Newsweek's list of the top hospitals in the country, none of the top five hospitals are in New York. The number one hospital is actually the Mayo Clinic in Rochester Minnesota.
Lorelei tells Luke "I am the yen to your yang, the Emack to your Bolio".
Emack & Bolio is a chain of ice cream stores based in Boston Massachusetts.
Anna tells Lorelai that April will not meet a man Anna's dating until she's ready to get married AGAIN, implying she's been married before.