Visible crew/equipment: When Emily enters the diner and says hello to Luke, two yellow T-marks are taped to the floor, then when she approaches the counter the actor's blue tape mark is visible at Luke's feet, and as Luke walks to the coffeemaker another tape mark becomes visible. (00:40:20)
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)
Answer: Yes, Lane lives with both her parents. Her father does live with them, but he was only seen in the Netflix revival.