At the beginning in this episode, Kirk says that he saw Luke and Lorelai kissing. But in the previous episode, Raincoats and Recipes (2004), at the end, you can see that when Kirk is running down the stairs, Luke and Lorelai are far away from kissing. So there's no way he could have seen them.
Lindsey tells Dean she found his phone, it had fallen between the couch cushions, and woke her up. When Rory called Dean's phone, it only rang once before she answered. If the phone woke Lindsey up and she had to search cushions before answering, it would have taken longer than one ring for her to answer.
When Richard and Emily first enter their basement, Emily stands near a large packing trunk. A few moments later she walks by the same area lugging luggage, and the trunk is gone.
In the very beginning, as Dean exits the Gilmore house, a man's reflection is clearly visible in the glass on the back door.
Visiting Rome, Emily mispronounces Piazza Navona as "Navano".
When Sookie comes downstairs to the basement, Lorelai calls her Squiggy.