The Fundamental Things Apply - S4-E5
Continuity mistake: Lorelai is in Luke's Diner talking to Luke. Lorelai is wearing a red sweater vest over a white blouse. When Luke is behind the counter, every time the camera faces Lorelai, the left side of her blouse goes from being tucked in under the vest (as if the vest were hastily put on), to being untucked (as it should be) quite a few times.
Ballrooms and Biscotti - S4-E1
Visible crew/equipment: A mic drops into shot while Lorelai and Luke talk about luggage and the cruise. (00:34:30)
Visible crew/equipment: When Lorelai is doing her baby-talk with "wittle Michel" he continues walking as she stops in front of Luke's, and the reflections of the camera operator and camera are visible on the glass door. (00:16:10)
Visible crew/equipment: When Lorelai is in the diner questioning Luke about Nicole, during their conversation the reflection of the boom operator holding both arms up is visible on the window. (00:21:40)
Ballrooms and Biscotti - S4-E1
Visible crew/equipment: When Sookie takes Lorelai out to the shed because Jackson doesn't want to know the sex of the baby, just as Sookie opens up the doors, we can see the hand of a crew member at the lower right side of the screen, stopping the moving door. (00:12:20)
The Fundamental Things Apply - S4-E5
Continuity mistake: While Lorelai and Michel are at the diner Luke tells Lorelai to take Michel elsewhere, and when Luke goes behind the counter his shirt is perfectly dry in this wideshot and following closeup. but in the next wideshot, as Lorelai tries to get Luke's attention, we now see a round wet spot on Luke's back, but the problem is Lorelai has not yet tossed the lemon wedge at Luke's back that causes the wet spot on his shirt. Lorelai tosses the lemon wedge about ten shots later. (00:07:25)
Continuity mistake: While Lorelai and Sookie are with Emily doing the test meal, when Emily tells Lorelai to remove the plates she picks up the two plates and walks out of the dining room, but in the next shot the plates have switched hands. (00:23:35)
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.