Those Lazy-Hazy-Crazy Days - S3-E1
Visible crew/equipment: When Lorelai and Rory are on their way to the festival they stop at Sookie and Jackson's house, and as they approach the front door, the reflections of the camera operator and camera are visible on the door's window. (00:25:05)
Visible crew/equipment: When Luke brings over the box of brownies for Lorelai he walks in and the front door is closed, then as they both walk away we can see the reflection of the boom pole moving on the door's glass. (00:13:25)
Back in the Saddle Again - S2-E18
Visible crew/equipment: When Rory and her classmates arrive at Richard and Emily's house Paris opens the door, and just as they reach the dining room, the two boom mics are visible at the top of the screen. Also note the huge crystal chandelier is conspicuously missing. (00:25:35)
Visible crew/equipment: At the end, when Luke walks into his apartment and passes Jess to get to the closet, we can see the reflection of the camera operator's legs in the bathroom wall mirror. (00:40:35)
The Bracebridge Dinner - S2-E10
Visible crew/equipment: During Friday night dinner, when they're discussing Emily and Richard's travel plans and then Richard's mood, in the wideshots from behind Emily lighting equipment is visible at the left side of the screen. (00:07:00)
Visible crew/equipment: While Dean is watching the play rehearsal, when Tristan starts talking about the "first kiss" in the wideshots facing Dean, we can see the boom pole moving at the top right corner of the screen. The boom pole is not part of the student production. (00:33:30)
Like Mother, Like Daughter - S2-E7
Visible crew/equipment: When the guidance counselor introduces herself to Rory during lunch she tells Rory to meet with her after lunch, and when she walks away camera equipment is visible at the bottom left corner of the screen. Then, at the end of the episode, when Lisa asks Rory if she can join her for lunch, the camera equipment is visible again before it moves. (00:06:00 - 00:43:15)
Star-Crossed Lovers and Other Strangers - S1-E16
Visible crew/equipment: While Lorelai helps her daughter get ready Rory holds up the two sweaters on hangers, and in the shot facing Lorelai as she tells Rory not to clash with the decor, lighting equipment is visible at the right side of the screen. (00:17:50)
Double Date - S1-E12
Visible crew/equipment: While Lane is trying to chat with Todd during the Double Date, when she asks if he likes Fugazi he tells her it's his sister's T-shirt, and just as Lane answers, "Oh," the boom mic dips a bit into view over Lane, at the top of the screen. (00:23:10)
Visible crew/equipment: While Lorelai is cleaning out the fridge, when she picks up the book and asks Rory to give the book back to Max, lighting equipment is visible at the right side of the screen.
Forgiveness and Stuff - S1-E10
Visible crew/equipment: When Lorelai and Dean are talking through Rory's open window, Lorelai tells Dean that they have a nice front door he might want to use, and when Dean walks away the moving boom pole is visible through the top of the glass window, in front of the lattice. (00:13:35)
Visible crew/equipment: After Rory asks Lane if Rich still wears the Star Trek shirt, when it cuts to Sookie in the kitchen, we can see two T-marks taped to the floor behind her. (00:08:40)
Visible crew/equipment: In the last shot, when Rory starts telling Lorelai all about the market kiss with Dean, some lighting equipment becomes visible at the right side of the screen, as the camera pulls back. (00:43:20)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Emily raves about Sookie's hors d'oeuvres, the shadow of the boom mic is bobbing around at the top of the screen. (00:35:10)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: When Lorelai gets home while Rory is on the phone, just as Lorelai jokes about Justin and Britney, filming equipment is visible at the left side of the screen. (00:06:35)
Kill Me Now - S1-E3
Visible crew/equipment: When Lorelai and Emily have a private chat about Rory playing golf with Richard, Lorelai tells her, "You win," and as Emily walks out of the room, the lighting equipment is visible at the left side of the screen. (00:06:00)
Visible crew/equipment: At the Kim house, when Lane and Rory reach the kitchen doorway, just as Mrs. Kim tells Lane that she has "muffins with no dairy, no sugar, no wheat," the boom pole dips into view at the top right corner of the screen. (00:11:35)
Visible crew/equipment: When April shows up at the diner, we can see the reflection of the moving boom pole and mic at the top of the window, behind Luke. (00:14:00)
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 Paris calls Rory while she's at the DAR office with Emily, in the shot of Paris as she walks away from the coffee cart toward the bench, a yellow tape mark is visible on the ground in front of the bench where Paris will sit. (00:13:40)
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.