Scene 1: Luke says he got a call from Kyle's father. How can Luke have gotten the call and be "sleeping in" if he is at the inn and getting ready to go skiing with Nicole?
While Rory and Lane are talking in the church, the rabbi enters and motions to the father to hurry up. The father starts to speak quickly, but when the shot goes back to Rory and Lane, he is talking at a normal pace again.
When Rory and Lane are in the church talking, the Rabbi walks in and the Reverend speeds up to finish church. However, Jewish people celebrate their Sabbath on Saturday night. The Rabbi and his congregants wouldn't have been at the church on Sunday morning.
When Lane is about to go to her room, a moment before the doorbell rings, a boom operator holding the boom mike can be seen in the glass door on the left side of the screen.
When Dave is standing on the porch outside of Mrs. Kim's, the shadow from the boom mike and pole can be seen.
When Luke confronts Jess' father, Luke yells at him for having abandoned Jess and Liz when Jess was just a baby. However, in Season 2 Nick & Nora/Sid & Nancy (2001), Luke had told Lorelai that Jess' father had walked out on them two years earlier.