When Lorelai is in the diner talking to Luke about his gloating behavior, two people (all dressed in black) walk by twice.
At about 18 minutes in, Lorelai is in the living room having drinks with Emily. Emily's hair changes throughout the scene. At times it's much fluffier and higher and at times it's slightly more tamed. You can generally tell this difference depending on who is on camera. When it's an individual shot of Emily, it is more tame. When it's a wider shot, it appears to be puffier. The style is the same, but it's just much fluffier. It's most noticeable near the beginning of the scene when Emily is at the drink cart. Her hair is very fluffy there, but in the first individual, closer shot of her it's a little more sleek.
When Lorelai and Rory are just about to order lunch at the inn, a woman wearing a denim jacket walks by twice.
When Lorelai is showing Christopher around the Dragonfly, Gigi is nowhere to be found. However, in the next shot, Gigi is with them at the table. It's highly unlikely that a random guest or Michel is looking after her while Christopher is touring the inn. Obviously Gigi couldn't just sit in the dining room alone either.
When Christopher comes for lunch at the Dragonfly, Rory is upset he's there and he tells Lorelei he needs to leave. Rory and Lorelei have lunch. Later when Lorelei is speaking to Luke she tells him that she and Christopher had lunch today with Rory and GiGi. Unless he came back and we didn't see this, he left long before lunch was served.
As Lorelai and Rory are leaving Emily's house, an inch of a camera lens is visible in the top left corner.