While Lorelai and Richard are arguing about colleges, the pen in Lorelai's right hand disappears and reappears, then the menus in her left hand disappear.
When Dean brings the car over to Rory's house, she sees him from inside through the window, and runs outside to greet him. She is not wearing a jacket when she looks out the window, and at 32:23 when she appears outside she is wearing a jacket but she is not shown stopping to put one on.
During Richard and Lorelai's argument, Richard claims that Lorelai has never once invited him to her house. Technically, this is true, because in the episode Rory's Birthday Parties (2000) (S1E6) it was Rory that invited Richard and Emily to the house for her birthday party.
Just after Lorelai and Richard come home after their day at the Inn and Lorelai hugs Rory, a camera man in a red shirt is visible in the reflection of the mirror behind Rory after Lorelai pushes her away.
(at around 48 mins) During Richard and Lorelai's argument, a boom mic is visible after Richard says the line "Suddenly I realise what it feels like to be a burden".
At the end of the fight between Lorelai and Richard, the microphone is visible above Lorelai's head.