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.
Continuity mistake: Lorelai and Sookie take some containers out of the car and head towards Emily and Richard's door. When you see the next shot of them at the door, the containers Sookie is carrying are different from the ones she took out of the car, without her rearranging them.
The Incredible Sinking Lorelais - S4-E14
Continuity mistake: Dean calls Rory, and towards the end of the conversation mentions getting his first cell phone. This is false. He's had a cell phone the whole series. Paris even calls it in the season 2 episode "Can't Get Started" when Rory and Dean are at Sookie's wedding.
The Fundamental Things Apply - S4-E5
Continuity mistake: When Rory comes into the room to answer the phone and sees Paris avoiding the call because it's her boyfriend Jamie, she empties the contents of her school bag onto the desk, including her mobile phone. Then later in the scene when Rory suggests Paris use her mobile phone to call Jamie, she pulls it out of her bag again, despite having left it on the table all but half a minute earlier.
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)
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)
Luke Can See Her Face - S4-E20
Continuity mistake: In this episode, Lorelai tells Luke that she needs to tell the plumber that rooms 10, 12, and 15 have no water pressure, but earlier in this season when she gives the presentation at the town meeting about the Inn to get her permits approved, she says that the inn will only have ten rooms. It is also mentioned in the last episode of the season when Lorelai puts her parents in room 12. (00:04:10)
Continuity mistake: In the scene where Rory is talking to Lane on her cell phone, she sits down on a bench. On that bench is a guy reading a book. The scene shifts to Lane in Stars Hollow, and when it shifts back to Rory at Yale, the guy on the bench is gone. (00:16:40)
In the Clamor and the Clangor - S4-E11
Continuity mistake: When Lorelai walks into Luke's apartment, she has a doughnut in her right hand, but as she's looking around the apartment and then leaving, the doughnut is nowhere to be seen. (00:25:16)
Continuity mistake: When Rory is sitting in the theatre, on the phone to Lorelai, we see the same people walk behind her twice - the woman with white jeans on and the woman with beige trousers. (00:42:10)
Continuity mistake: Right before Lorelai goes outside of the Dragonfly to talk to Jason you can see she is standing behind a desk, then later Michel says that he is sick of sitting on the floor and wonders when the desk is coming.
Continuity mistake: During the phone call between Emily and Lorelei about the grandmother's passing, the ceramics on the table change positions many times.
Continuity mistake: While Lorelai is at the diner talking to Luke about Nicole, when she takes a seat at the counter she places her black purse on the stool beside her, but in the following shots that purse repeatedly reappears and disappears from her shoulder, depending on the camera angle. (00:23:25)
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.