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)
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).
Continuity mistake: When Lorelai tells Rory she doesn't have to go into the Dean of Admissions' office, Emily is standing right next to her but when Lorelai turns to step away from Rory, Emily is many steps back.
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.