At the baby shower, Lorelai says her main inspiration for raising Rory was For Keeps?, the 1988 Molly Ringwald movie about teen pregnancy. But based on Rory's age in the show, she was born around 1984 or '85, meaning the movie would not have been out yet.
At the baby shower, no one is supposed to say the word "baby". Yet, during the game where they are shoving cotton balls into the bag, Sherry continually says the word baby and no one takes her pin or corrects her.
Kirk complains about not being allowed to drive a car, but in Gilmore Girls: I Can't Get Started, his car was blocked in by Christopher's Volvo at Sookie's rehearsal dinner. Clearly, he was driving at some point.
When Rory and Lorelai are egging Jess's car, they only throw them at the front part of it, including the hood and windshield. However, the next morning there are deviled eggs all over his car, including the side doors and windows, as well as the trunk.