When Rory is upstairs in Luke's apartment, she asks Luke where Jess is and between shots the sleeves on her shirt go from being pulled all the way down to being pushed up around her elbow.
When Emily came to the Inn to help Sookie's wedding she addressed Lorelai as Richard.
At 6:50, the camera shows the town bard to begin a scene change, and Lorelai and Rory are visible in the background waiting for their cue to start walking.
Right after Rory knocks on the door to Luke's apartment, a cord of the equipment is visual on the right hand side of the screen.
When Rory shows up in Luke's apartment, a boom mike is visible in the mirror behind her.