Visible crew/equipment: After Luke catches Rory and Jess together Rory rushes out, and while Luke is lying down all the ground rules for Jess, the T-mark is visible on the floor near the door. (00:16:15)
Haunted Leg - S3-E2
Visible crew/equipment: After Lorelai and Rory meet Emily's new maid, when they walk into the living room the T-mark is visible on the floor where Emily stands. (00:32:05)
Those Are Strings, Pinocchio - S3-E22
Visible crew/equipment: When Lorelai, Sookie, and Jackson are "celebrating" they all sit down at the table, and we can see the T-mark on the floor behind Jackson. (00:11:30)
Revealing mistake: While Rory and Lorelai are in the kitchen, in a few closeups of Rory we see the refrigerator and counter area with the microwave, etc. behind Rory, but when Lorelai is at the back door about to join Luke, part of the set beside the refrigerator is gone. (00:04:15)
Say Goodnight, Gracie - S3-E20
Visible crew/equipment: When Luke gets home Jess confronts him about seeing his father, then just as Jess walks behind Luke the two T-marks are visible on the floor. (00:38:15)
Say Goodnight, Gracie - S3-E20
Visible crew/equipment: After Lane apologizes to Mrs. Kim in the kitchen, when Lane walks to the stairs as the doorbell rings, the reflection of the boom operator holding the boom pole is visible on the glass. (00:29:45)
A Tale of Poes and Fire - S3-E17
Visible crew/equipment: When Lorelai has the house-guests due to the inn's fire, Fred Jr. is sitting on the couch and calls her ma'am, then as Lorelai tells the boy to stop because it makes her feel old, the boom mic dips into view at the top of the screen. (00:27:30)
Visible crew/equipment: After dinner with Emily, when it cuts to Lorelai and Rory rushing into their house, an equipment pole is visible at the right side of the screen at the start of the shot, and a standing spotlight lamp is reflected in the wall mirror. Then as Lorelai walks back down the stairs the camera is visible at the left side of the screen, and when Lorelai exits, the spotlight lamp's reflection is visible again. (00:06:25)
Visible crew/equipment: When Lorelai returns from her trip she tells Rory that she needs food, and as they walk away from the car, we can see the reflections of the camera operator, camera, and boom mic moving on the surface of the car. (00:38:30)
Visible crew/equipment: While Dave, Brian, and Zack are in the car, when Mrs. Kim is speaking to Dave the reflection of the boom pole is visible in the window behind Mrs. Kim, then after she leaves when the car starts moving, the reflection of the reflector screen is also visible in Brian's window. (00:31:15)
Continuity mistake: When Loralie is having lunch with Paris, as Paris is leaving at about in Lorelai is wearing tennis shoes. As she walks into the kitchen she has heels on. (00:09:00 - 00:10:00)
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)
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: This was in season six in the Martha's vineyard episode (Valentine's day). Lorelai comes into the kitchen and we see a shot of Rory cooking. Next to her is the orange juicer. In the next shot, it is not there. It reappears as Lorelai is watching Rory cook and Rory reaches into a drawer and pulls it out.
Back in the Saddle Again - S2-E18
Continuity mistake: When Lorelai sits down with Dean to discuss how "clingy" he is with Rory, both Lorelai and Dean's hand positions change between shots, specifically whether their fingers are laced, resting normally on the table or raised in the air.
Visible crew/equipment: During the Friday night dinner, something that looks like a microphone swings back and forth next to Richard's arm. It is most visible in the first shot of him (from behind).
Richard in Stars Hollow - S2-E12
Visible crew/equipment: At one point during Lorelai's argument with Richard at the end of the episode, a boom mic is visible above Lorelai's head. (00:40:25)
Other mistake: In the opening scene, Lorelai and Sookie go to the bakery to pick up a cake. Lorelai pays for the cake but they leave the bakery empty-handed.
Continuity mistake: When Lane delivers lunch from Luke's to Rory in the bookstore, the couple seen outside (man in black jacket and woman in white coat) are seen approaching and picking up a magazine not once but four times. They re-approach and pick up the magazine in each camera shot of Lane. (00:27:45)
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.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.