Continuity mistake: Logan puts his computer tablet on the sofa cushion with the Windows logo down; when he leaves, the logo faces up.
Continuity mistake: When Rory sits on her bed in the hotel room, her bag changes position.
Other mistake: Luke and Lorelai are talking in the diner. Lorelai asks Luke if he ever wanted a fresh kid. Lorelai then says to him "you'll never get to go to your kid's graduation." Are we to believe that Luke didn't go to April's high school and college graduations?
Continuity mistake: In the original show we are led to believe that Lorelei lost her virginity to Christopher. But in this, during the late night gathering outside after the funeral, Lorelei's story about her father was about her losing her virginity to someone who wasn't Christopher. She got pregnant at the age of 16. We are to assume that she did not sleep with anyone immediately after Christopher. If the above is true, she didn't get pregnant when she lost her virginity. If she didn't get pregnant then she should've been safe with Christopher. What did the above were true, we would have heard about it. She would have told her daughter about how she lost her virginity.