Visible crew/equipment: When Lorelai returns from her trip she tells Rory that she needs food, and as they walk away from the car, we can see the reflections of the camera operator, camera, and boom mic moving on the surface of the car. (00:38:30)
Visible crew/equipment: While Dave, Brian, and Zack are in the car, when Mrs. Kim is speaking to Dave the reflection of the boom pole is visible in the window behind Mrs. Kim, then after she leaves when the car starts moving, the reflection of the reflector screen is also visible in Brian's window. (00:31:15)
Chosen answer: Lorelai and Christopher get married impulsively in Paris but they get divorced shortly after returning home. I don't know the exact number of days or weeks but they definitely weren't married for more than a couple of months.