Rory's Birthday Parties - S1-E6
Visible crew/equipment: After Rory takes Tristan's invitation and walks away, when it cuts to Emily and Lorelai shopping at Damion's, just as Emily notices the hat we can see the crew member and equipment at the right side of the screen. Then, when Emily finds the light-up bracelets and shows Lorelai, some lighting equipment is visible at the left side of the screen and cables are on the floor behind them. (00:08:30)
Rory's Birthday Parties - S1-E6
Visible crew/equipment: At Chilton, when Rory walks past the girls talking about another obligation party, in the next shot facing Rory we can see lighting equipment at the right side of the screen. (00:08:20)
Visible crew/equipment: While Rory is at Luke's doing her homework, when Lorelai walks in and is about to sit down at the table with Rory, the lighting equipment is visible at the right side of the screen. (00:19:50)
Visible crew/equipment: When Lorelai talks to Emily at the Independence Inn, a boom mic briefly drops into the shot. (00:21:25)
Continuity mistake: The appearance of the Gilmore mansion is very different in this episode than in following episodes. Here there are steps leading up to the front door, but none in later episodes, and the area people park their cars changes significantly as well.
Rory's Dance - S1-E9
Factual error: The morning after Dean and Rory fall asleep at Miss Patty's, when Patty wakes them up, she tells them it's five-thirty in the morning. When Rory runs out into the street, there is snow on the ground and the sun is up. In Connecticut, there is no time of year in which there would be both snow on the ground and sunlight at 5:30 a.m. (It's not streetlights either - in other episodes that take place at night in the town square, the streetlights do not light up the entire square - they are some distance apart, and their light is concentrated around the poles).
Continuity mistake: In the opening scene Lorelai crosses the street to Luke's which is in the middle of the block instead of on the corner of the block.
Continuity mistake: In the shot where Lorelai and Rory are in Luke's diner, after Lorelai moves her burger in front of her, the plate changes positions several times between shots.
Continuity mistake: In the opening scene, and all episode, Luke's diner is considerably smaller than the rest of the series. He has a shelf with random hardware and fishing items that is a window the remainder of the series.
Visible crew/equipment: When Paris drops her book on the floor in English class, to jolt Rory out of her daydream stupor, a boom mic is visible above Liza Weil's head. (00:16:45)
Double Date - S1-E12
Other mistake: When Rory and Lane get caught at the movies, Lorelai said she will not lie to Mrs. Kim because she has to respect that Mrs. Kim doesn't want Lane to do something. In reality, Lane is allowed to do things Mrs. Kim would not approve of all the time i.e. Listening to ungodly music, eating pizza, wearing different clothes.
Rory's Birthday Parties - S1-E6
Visible crew/equipment: While Emily is instructing the servants before the party, when she tells one servant, "I want those six inches apart, get a ruler," there are two problems with this medium shot. First, lighting equipment is visible at the top right side of the screen over the lamp, and second, it's a flipped shot. Note the painting and lamp are reversed in the medium shot, compared to the next wideshot which is fine. (00:17:45)
Love, Daisies and Troubadours - S1-E21
Continuity mistake: When Lorelai tries to remember the name of the guy who used to run the auto-body shop, she opens the kitchen's back door in the interior shot, but in the next exterior shot Lorelai is walking out of the side living room door, with the window beside it. (00:06:15)
Continuity mistake: At Luke's, when Rachel shows Lorelai the photo of the Dragonfly Inn, Rachel says, "It's an old abandoned inn I ran across when I was exploring the other day." So Rachel took the photograph in the last few days, and in the photo the Dragonfly does not have shutters, and does not have a sign hanging over the porch, etc. When Lorelai visits the Dragonfly with Rachel and then with Rory, the shutters and sign have appeared, as well as other changes. (00:04:50 - 00:40:20)
Continuity mistake: At the start, during dinner things on the sideboard move between wideshots and closeups of Rory. Fun to note: when Emily gets up and follows Richard to his seat, as Emily shouts to Siri that Mr. Gilmore is hungry, the camera pans a bit to the left and a water bottle (it's gone in Rory's closeups) has been placed on the sideboard, beside the sterling bud vase, which would cause Emily to have a fit. Obviously one of the actors or the crew left it there.
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)
Other mistake: After Lane goes home, when Rory watches her mom talking to Max note the short window over the kitchen sink behind Rory (not the tall window on the same wall). In the next shot, from outside that short window, we see Rory pull the photo strip out of her pocket then proceed to walk to that window and stand directly in front of it. The problem is there should be a sink and cabinets under that window blocking Rory from standing beside the window. (00:43:05)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.