As Rory is in her dorm room talking to Lorelai, Lane is in the background alternating between wearing and holding her coat as the shot changes.
When Luke and Liz are upstairs in the diner, he pours a glass of juice, drinks it and puts the bottle back in the fridge. The glass then appears with more juice.
At Emily's house before Friday dinner, the pendant on Lorelai's necklace changes position between shots.
After Lorelai talks to Emily on the phone, her hair keeps changing between 'on the shoulder' and 'behind the shoulder.'
When Rory is packing to head back to Stars Hollow and is talking to Paris. At one point (on the widescreen Netflix version), on the right side of the screen you can see where the set ends.
Paris tells Rory that she's always loved English accents and gives as an example the fact that "as a kid she was in love with Neil Kinnock" (leader of British Labour Party during 1980s). Neil Kinnock is actually Welsh and has a very distinctive Welsh accent rather than an English one.