In earlier episodes, it's explicitly stated that Rory is 16 years old. She has had a birthday since then, thus making her 17 (there were even 17 candles on the cake), yet when Lorelai is talking to Dean at the window, she asserts that Rory is 16 now, as if the birthday episode hasn't happened yet.
In the beginning, when the camera is on Lorelai, it is daytime outside, but when the camera is on Rory, it is nighttime.
At the hospital after Richard is returned to his room and Lorelai is avoiding going into the room, the boom mic drops into the scene as she says, "You know what hurts? A screwdriver in your head."
When Dean leaves the Gilmore porch, a boom is visible in the upper left.