Audio problem: In the scene where Lorelei and Rory are sitting at a table, with Rory looking at herself in a mirror, they talk about Rory's hair. Right after this, Rory asks, "do you want something to drink?" Her mouth doesn't move at all.
Visible crew/equipment: In the scene where Rory asks Lorelai to call Emily to get her out of Friday Night Dinner so she can celebrate her and Dean's 3-month anniversary, a boom mic drops into the shot as Lorelai stands to get the phone.
Continuity mistake: When Lorelai, Rory and Max are having breakfast at Luke's, their coffee cups change from red to blue in one shot. Also Max's coffee cup goes back and forth from the left side of his paper to the right.
Trivia: In some episodes, Rory speaks Spanish (e.g when she is talking to her grandmother's maid). She speaks very poorly, typical "school-Spanish". This is just acting; Spanish is actually Alexis Bledel's first language. Her mother is from Mexico and her father is from Argentina.