When Rory is talking to her grandmother as she's about to leave the house, she's seen wearing both a dark red lipstick and a mauve-colored/dusty rose colored lipstick, interchangeably, throughout the conversation.
When Luke and Lorelai is at the diner and Luke is telling the girls on the soccer team that he will sponsor them, Lorelai is flipping through her color samples. As she starts to turn around she has stopped only about a quarter of the way through and on a yellow paint swatch. The camera then turns to face her as she starts talking. As she is talking, she is about halfway through the stack and she has stopped on a blue paint swatch.
When Jess arrives at Rory's grandparents' house, Rory has just come back from driving Logan, Finn, and Colin home after the bar in New Haven had closed. Bars close very late at night, so it's probably around 3 AM, which is a very strange time of day for Jess to make a surprise visit.
When Rory puts drunk Logan into her car, the reflection of the mic is visible in her windscreen.
When Lorelai tries to convince Luke to sponsor the soccer team, she says it would be "free advertising". Luke sponsoring the team would NOT be free - he'd have to pay for the jerseys and, therefore, the advertising.