It's Just Like Riding a Bike - S7-E19
Plot hole: The dog, Paul Anka, uses the porch steps without a blanket over them. In an earlier episode, Lorelai states that he's afraid of the porch steps when Babette tries to walk him. (00:32:50)
How Many Kropogs to Cape Cod? - S5-E20
Character mistake: On the first day of Rory's internship, she is told she needs to get an ID, to which she replies she never had an ID before, but she got an ID during her first day at Yale, which she and friends later pretended to lose to get new ones.
Continuity mistake: Rory's snow-cone changes color from deep red to light pink between shots.
Lorelai's Graduation Day - S2-E21
Continuity mistake: When Emily, Lorelai and Richard are going to take the picture, Richard lifts his arm as if he is going to put it around Lorelai's shoulder. The angle changes and his hand is no longer raised. He then raises it again before finally lowering it.
Factual error: This episode takes place in Connecticut in February. When Luke and Lorelei are leaving her house to go to the Vineyard, they are not wearing coats, there is no snow, and all the trees have leaves and plants are in bloom.
Visible crew/equipment: Near the end of the episode when Rory comes home and is standing on the porch talking to Lorelai at the door, right before Rory says "Hi" you can see a crew member in the background, standing in the bushes on the other side of Lorelai's jeep and then moving out of sight (toward the left side of the screen). (00:39:20)
Dear Emily and Richard - S3-E13
Factual error: When Lorelai arrives at the hospital, Rory says she is xeroxing a report that she needs to fax for Sherry because Sherry didn't make enough copies. No matter how many people the report needed to be faxed to, only one original copy would be needed.
Visible crew/equipment: A mic drops into shot just as Jackson accepts Sookie asking him on a date. (00:38:45)
Character mistake: In this episode, Rory tells Lorelai that she was cleaning her computer's hard drive because it was full of unopened downloaded files which were consuming her CPU speed. This is wrong, the situation which she's explaining would not use up any extra CPU speed - she may be trying to say her hard drive was extremely fragmented which MIGHT consume some CPU speed (but a tiny amount).
Rory's Birthday Parties - S1-E6
Visible crew/equipment: As Lorelei climbs into bed with Rory at 4:03 there is what appears to an open book being lowered out of the shot by a presumed crew member.
Nick & Nora/Sid & Nancy - S2-E5
Audio problem: When Lorelai is speaking to Luke about bringing Jess into Luke's home, her "the great communicator" line still has scratch audio attached.
The Lorelais' First Day at Chilton - S1-E2
Continuity mistake: While Rory is at the administration office Miss James gives her the Chilton map, schedule, etc. Then just as Miss James tells Rory that Mr. Winters, the guidance counselor, handles everything except bulimia and pregnancy, Miss James is wearing eyeglasses in the shot facing Rory, but in the previous and following shots she is not. (00:15:50)
The Big One - S3-E16
Visible crew/equipment: When Lorelai and Rory are at Richard's while Emily is away visiting her friends, Richard steps out to answer a call. When Richard returns we can see a blue T-mark taped to the floor behind Rory's side of the sofa. This T-mark is visible again when Richard asks about Rory's speech, because he'd like to be there. (00:20:00)
The Big One - S3-E16
Continuity mistake: When Lorelai sits down on the porch swing at Suki's house to talk, they are both sitting right next to each other, sharing the same blanket. During their conversation, when the shots face each of them individually, you can see there is an empty space beside them on the swing, with both sides of the swing's chains visible. (00:20:50)
Lorelai's Graduation Day - S2-E21
Continuity mistake: When Rory and Lorelai are talking in their kitchen, Rory pushes the cafetière plunger down but then over the conversation it is pictured sometimes raised, and then lowered and then raised again a few different times. (00:04:30 - 00:06:00)
In the Clamor and the Clangor - S4-E11
Continuity mistake: When Lorelai walks into Luke's apartment, she has a doughnut in her right hand, but as she's looking around the apartment and then leaving, the doughnut is nowhere to be seen. (00:25:16)
Continuity mistake: When Rory is sitting in the theatre, on the phone to Lorelai, we see the same people walk behind her twice - the woman with white jeans on and the woman with beige trousers. (00:42:10)
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)
Visible crew/equipment: When Rory is dropped off in the morning, he walks up the front porch, Lorelai greets her at the door. Behind Rory across the driveway in the bushes is a man. The many slowly hides back into the bushes. (00:39:19)
A Messenger, Nothing More - S5-E2
Continuity mistake: Lorelai's hair is once curly, once straightened in every other shot after she leaves her house with Rory up until she meets Luke. (00:31:45)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.