Visible crew/equipment: At the start of the episode Rory and Lorelai are about to open the garage door. You can see a crew member in the reflection of the glass moving his arms around the camera - you can also slightly see his head for a split second. (00:39:00)
Continuity mistake: When Luke knocks on the kitchen door (at the back of the house) and calls Lorelai out to talk on the back porch, Lorelai grabs the doorknob to go out that door, but in the very next shot from outside Lorelai is actually walking out of the side living room door which is at the side of the house while Luke is standing there. Two completely different doors, at different sides of the house, and the back porch is not connected to the side/front porch. (00:06:10)
The Big One - S3-E16
Visible crew/equipment: At Chilton, after the teacher returns the graded papers to the students, when she walks to the front of the class her T-mark is visible on the floor. (00:04:55)
Eight O'Clock at the Oasis - S3-E5
Visible crew/equipment: When Emily gives Lorelai and Rory their drinks she mentions the cheese and walks away, then when Lorelai sits on the sofa the green tape marks are visible on the floor, where Emily had been standing by the bar. (00:40:20)
Haunted Leg - S3-E2
Visible crew/equipment: After Emily tells the new maid it would wonderful to remember the difference between the bells, as Emily, Lorelai, and Rory walk away from the front door, the white, red, yellow, and green tape marks are visible on the floor behind them. (00:32:00)
Haunted Leg - S3-E2
Visible crew/equipment: When the new maid tells Emily the dinner is ready even though it's only 6:30, Emily concedes and they all head to the dining room, and just as Emily says they all can be in bed by 9:00, we can see the boom pole and mic in the living room behind them, at the top of the screen. (00:33:20)
The Big One - S3-E16
Continuity mistake: In 1.06 - "Rory's Birthday Parties" Paris says "Ten generations of Gellers have gone to Harvard". In this episode Paris says "Five generations of Gellers have gotten into Harvard"
Visible crew/equipment: When Jess shows up at Principal Merton's office because he couldn't get prom tickets, as Jess shuts the office door the hand of a crew member is visible between the door and frame, slowing the moving door. (00:14:30)
Continuity mistake: In the scene where Luke and Jess are on the lake discussing in the end, when the camera is on Luke they are in the sun and when it is on Jess they are in the shadow.
They Shoot Gilmores, Don't They? - S3-E7
Visible crew/equipment: Before the dance marathon, when Lorelai and Rory are headed over to the first aid station they meet up with Sookie, and when Lorelai and Sookie cross the street we can see the T-marks taped to the sidewalk. (00:15:15)
Those Are Strings, Pinocchio - S3-E22
Continuity mistake: During the graduation Lorelai borrows Richard's pen and writes "we got the inn" on the graduation program, and when she holds the program up to show Rory note the position of the blue logo printed on the bottom page. First the logo is near the center crease, but then it's at the outer edge of the page. (00:35:20)
Visible crew/equipment: When Richard walks into the dining room with the treat for the masses and serves Rory this special dish, we can see the boom mic bobbing about in the reflection on the window, at the left side of the screen. (00:00:15)
Visible crew/equipment: When Lorelai and Rory walk into the living room while Emily is on the telephone with her lawyer, the filming equipment is visible at the right side of the screen. Then when Emily walks over to the bar to pour a drink, the T-mark (looks like chalk) is a bit visible on the floor where she stands. (00:00:25)
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)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.