Sadie, Sadie - S2-E1
Continuity mistake: At the diner, when Lorelai stands at the counter telling Luke about Max's proposal, in the shots facing Lorelai we see the red ketchup bottle on the table behind her is either standing upright or lying on its side, changing a few times. (00:07:05)
Sadie, Sadie - S2-E1
Continuity mistake: When Richard enters to announce Rory being in the top 3% in her class his handkerchief is shown with 1 point. When he then walks to pour a drink and turns around, it has 2 points showing.
Sadie, Sadie - S2-E1
Continuity mistake: When Lorelai and Rory get home from the upsetting dinner from Richard attacking Dean, while sitting at the table one shot shows the Twinkies arranged on the plate in front of Rory on the table. In a few other shots, you see a few twinkies missing and not arranged.
Red Light on the Wedding Night - S2-E3
Continuity mistake: When Rory and Lorelai are testing cakes for the wedding at Fran's bakery, Rory is seen taking pieces out of the raspberry cake several times. However when the angle changes you can see that the cake is whole as if none of it had been eaten. (00:00:45)
Red Light on the Wedding Night - S2-E3
Continuity mistake: When Lorelai, Max, and Rory are in the diner, just as Luke tells them that he's almost out of the blueberry pancakes and he can't make more, the regular menu which is set upright on the table suddenly becomes the "lunch" menu, and then it's back to the regular menu. This occurs well before Luke even brings Max the lunch menu because Max is taking too long to decide. (00:13:35)
Red Light on the Wedding Night - S2-E3
Continuity mistake: When Lorelai, Rory and Max are having breakfast at Luke's, their coffee cups change from red to blue in one shot. Also Max's coffee cup goes back and forth from the left side of his paper to the right. (00:14:50)
The Road Trip to Harvard - S2-E4
Continuity mistake: When Lorelai returns to Stars Hollow she goes to Luke's, and as she takes a seat at the counter there's a glass domed cake platter (with what looks like pie) at the end of the counter, which promptly vanishes in the following shots. Also, the blue box of wax paper sheets moves to the opposite side of the hot cups on the counter, between shots. (00:37:55)
The Road Trip to Harvard - S2-E4
Continuity mistake: When Luke offers Lorelai coffee, Luke grabs two paper hot cups, but the camera angle shifts and he is holding only one cup, then the angle shifts again and he is back to having two cups while he proceeds to pour the coffee. (00:38:10)
The Road Trip to Harvard - S2-E4
Continuity mistake: When Rory tells Lane about what she saw at Harvard, she comments, "where I might live next year." But earlier, Rory says that she's still two years away from Harvard.
The Road Trip to Harvard - S2-E4
Continuity mistake: Before Lorelei leaves the diner at the end, there is a dirty coffee mug at the end of Luke's counter, but when she leaves, the mug is gone.
Nick & Nora/Sid & Nancy - S2-E5
Continuity mistake: During dinner, when Jess takes the beer from the fridge he walks out the kitchen's back door which has a lattice wall on the porch, and when Lorelai opens the same door, in the next exterior shot she's walking out the side living room door, onto the porch. (00:26:20)
Nick & Nora/Sid & Nancy - S2-E5
Continuity mistake: When Rory interviews Max, in each shot the pens on his desk in the cup keep rearranging.
Presenting Lorelai Gilmore - S2-E6
Continuity mistake: During the presenter's introductions at the start of the ball, there's a shot of Lorelai from behind while she's seated alone at the table and we see the glistening necklace around her neck, but in the following shot facing Lorelai as she turns her head toward her parents the necklace has vanished, then she gets up and as Lorelai walks toward Emily and Richard the necklace has reappeared. (00:31:25)
Presenting Lorelai Gilmore - S2-E6
Continuity mistake: When Lorelai calls Chris to tell him about Rory's debut, she writes his new number on a gum wrapper. The shot changes to Rory. When it cuts to Lorelai again, she is reading the number from a notebook.
Presenting Lorelai Gilmore - S2-E6
Continuity mistake: When Christopher comes to the house and they are all outside talking, there is no garage on the side of the house. Only gates. In later episodes there is a garage.
Like Mother, Like Daughter - S2-E7
Continuity mistake: When Mr. Charleston is looking at Lorelei's parent file, he closes it and starts talking and in the next shot he is seen closing it again.
Continuity mistake: Lorelei's casual date brings his parents into Luke's and even though the windows are covered and you can't see outside, the cash register is at the wrong end of the counter.
The Bracebridge Dinner - S2-E10
Continuity mistake: When Dean and Clara first arrive at the Inn and are shown talking to Rory, Luke and Jess arrive in the background and Luke removes his jacket. In the next shot his jacket is back on and he removes it again.
The Bracebridge Dinner - S2-E10
Continuity mistake: When Rory is checking in Lane and Mrs Kim, twice in a row it shows her close her folder and hold it at her side and in the next shot it is still open.
Continuity mistake: When Lorelai puts her book bag on the table there's an economics book showing and in the next shot it is gone.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.