When Rory is sitting on the bus from New York to Stars Hollow, the cast on her left arm is gone when she's talking to another passenger. The next time we see Rory at the Gilmore house in Stars Hollow, her cast is back.
At the beginning when Rory and Lorelai are sitting at the table, the French Press switches between being drawn up and pressed down.
When Rory is talking to Jess when he called from New York, a digital clock appears on her nightstand at the end of their conversation.
When Emily, Lorelai and Richard are going to take the picture, Richard lifts his arm as if he is going to put it around Lorelai's shoulder. The angle changes and his hand is no longer raised. He then raises it again before finally lowering it.
The amount of coffee in the French press Rory is holding changes as she moves it from the table.
In the record store, a customer says Slint disbanded in 1994. Slint actually disbanded in 1990 after Spiderland was finished. The single referenced was released in 1994, so these were both released post-breakup.
In the record store when Jess asks who Slint is, someone says they are a grunge rock band. They are actually a post-rock band with post-hardcore influence, not grunge.