Character mistake: This mistake happens in the town meeting scene. They are talking about the two business owners that dated, then moved when it ended badly. It hurt the town's economy. First it was said that Faye sold flowers and the guy sold candy. Then they said that Faye sold candy.
How Many Kropogs to Cape Cod? - S5-E20
Character mistake: On the first day of Rory's internship, she is told she needs to get an ID, to which she replies she never had an ID before, but she got an ID during her first day at Yale, which she and friends later pretended to lose to get new ones.
Character mistake: In this episode, Rory tells Lorelai that she was cleaning her computer's hard drive because it was full of unopened downloaded files which were consuming her CPU speed. This is wrong, the situation which she's explaining would not use up any extra CPU speed - she may be trying to say her hard drive was extremely fragmented which MIGHT consume some CPU speed (but a tiny amount).
Dear Emily and Richard - S3-E13
Character mistake: Lorelai calls Rory "Suki" when they are unboxing the books Emily gave to them. (00:10:08 - 00:31:11)
Suggested correction: She calls her "sweetie."
Character mistake: While Rory is on the phone discussing a DAR application, Emily enters. Rory asks the caller to hold, but she doesn't hit a button to put the call on hold. She put down the receiver disconnecting the call. Then she forgets that she has someone on hold.