Continuity mistake: After the opening credits, Lorelai is watching TV in the kitchen. After she picks up the remote control, the camera angle changes and the TV is gone. It then reappears when Lorelai is standing by the stove. (00:02:35)
Continuity mistake: Kirk did not know who Miss Patty was. He said "I wasn't aware that you were THE Miss Patty." Later in the series, in Episode 5 of Season 6, at Miss Patty's Grand Recital, Miss Patty introduces Kirk's performance and says that he was "a talented pupil of mine". His performance was titled, "20 Years Ago Today", therefore Kirk was a student and should have known who Miss Patty was all along.
Continuity mistake: In S1E3 "Kill Me Now" when Babette tells Lorelai that Cinnamon is stuck under the porch again, she refers to Cinnamon as "him", but in this episode Babette talks about Cinnamon being female.
Suggested correction: That's exactly the point of the scene. Kirk knew that her name was "Miss Patty" but he didn't know she was THE "Miss Patty" about whom everyone was speaking.
They also refer multiple times to Kirk growing up in Stars Hollow. He would have known. In Stars Hollow, there couldn't ever be another "Miss Patty." That's just not how they roll.