When Luke is getting Lorelai coffee, he grabs the to-go cups. In the first shot, there are two cups together in his hand, then the shot changes and there is only one cup. Then the shot changes again and he is putting a lid on, and there are two cups again.
At Harvard, when Lorelai leaves Rory at the lecture hall, she says something about someone putting "an aspirin in my coke". Rory responds with "Okay, Rizzo", referring to the character in "Grease". However, in "Grease" it is Marty, not Rizzo, who catches someone putting aspirin in her coke at the dance.