Twice Luke is shown walking to the diner early in the morning to open up. Later it is established that Luke lives in an apartment above the diner and has for a long time.
When Rory and Christopher go into Luke's after Jackson runs away from them, they enter from the opposite direction to what Jackson was running.
At the end of the episode, Luke walks into the diner to find Lorelai has painted without him. When he enters, he closes the door behind him. This is seen and the bell can be heard when the door closes. But, the closing shot of the episode shows Lorelai and Luke in the diner talking about curtains. As the camera pans out, the door is standing wide open despite no one else having entered the diner and neither Luke nor Lorelai have opened it.
Near the beginning with Lorelai is explaining to Sookie that Christopher is in town, she says that she hasn't seen him since last Christmas. Last Christmas, she was in town with Luke having been told not to come by her mother until her father is sent to the hospital. There was no way that she would/could have seen Christopher and this is his first appearance.
During Dean's softball game it is very clearly raining. You can see visible raindrops several times. The bleachers that they are sitting on are wet. The raindrops on umbrellas is clearly audible as well in the background. But everyone is dressed for normal weather (dry clothes), and not acknowledging that they have wet bums sitting on those bleachers.
When Christopher leaves the Gilmore house, we see shots of the driveway from every angle. But the way the set is dressed, there is no access to the street; the driveway ends in a wall.
When Luke is outside his diner waiting for Lorelai, the cameraman and crew are visible in the window.
When Dean walks off of the baseball field toward Rory and Christopher there is a palm tree visible in the background.
After Lorelai surprises Luke by painting the diner overnight, she suggests curtains and Luke replies by saying no. There are already curtains hanging on the bottom half of all the windows.
When Jackson introduces himself to Christopher, he clearly says, "Jackson Melville," but in future episodes his name is Belleville.