Other mistake: Season 6, 9/20/05, "Fight Face"While in Luke's Diner, Luke hands Lorelei a cup of coffee in a 'to go' cup. When Luke puts the coffee in front of Lorelei, the cup makes a hollow sound when it hits the counter, obviously indicating that there's no actual coffee in the cup.
Plot hole: In the episode when Jess arrives at Luke's, Luke explains to Lorelai that Jess' father walked out on his family two years ago. Jess is 17 at that point, which would make him 15 when his father left. In the episode where the father comes to see him, Luke asks him why he left when Jess was just a baby in diapers, and indicates that he hasn't seen him since.
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.
Character mistake: Season 5, Episode 3 - "Written in the Stars": This mistake happens in the town meeting scene. They are talking about the two business owners that dated, then moved when it ended badly. It hurt the town's economy. First it was said that Faye sold flowers and the guy sold candy. Then they said that Faye sold candy.