While Emily is on the phone with Lorelai, a vase on the table moves around between shots.
When Lorelai is talking to Emily, who is drinking and smoking, Emily's hair switches from behind her ear to over it in between shots.
While the patrons of Luke's Diner are listening to Luke and Nicole fight, you can see Miss Patty standing a few feet outside the door, waiting for her cue to enter.
When Richard is talking to Emily after the funeral, he calls his mother Gran. He only caller her Trix, and it doesn't make sense for him to call her Gran, since she was his mother.