In considering offers from Harvard and Yale Law, Paris makes reference to Harvard being the best law school nationally. However, Yale is actually ranked #1, Harvard is second.
When Rory is opening Paris' letters, she goes to use the letter opener on the one from Columbia. She barely uses the letter opener then the unsealed flap opens and that's how she pulls the letter out.
When Luke and Lorelai are car shopping and Lorelai is sitting in the Jeep, you can see the crew in the side mirror when she opens the door to get out.