Continuity mistake: The door to Mrs. Krabappel's classroom has a window, but when Bart fakes being sick then walks out of the class (we see the desks as the door closes), the door's window has vanished, and the doorknob has switched sides as well. Additionally, earlier, when Bart deliberately falls off his chair in class, note that one of the bars on the back of his chair has gone missing. (00:07:35)
Continuity mistake: When Bart hands Ms.Krabbappel his final test, there are some shots going back and forth between their faces. During the first shot looking at Ms.Krabbappel, you can see a window behind her, and outside the window, there is no snow, even though there was a whole lot of it yesterday. During the next shot, the snow IS there. As the camera goes back and forth, the snow disappears and reappears.
Continuity mistake: Just before Bart's flashback, his shirt is orange, and the chair he's sitting on is blue. But in this episode, his shirt is a paler shade of orange and the chairs in the classroom are red.
Continuity mistake: When Bart fails the test despite having actually studied, we see the two red "X" marks in the center row of the multiple choice questions, but after Mrs. Krabappel passes Bart because he applied practical knowledge, when Homer hangs the test up on the fridge those two "X" marks in the center have vanished.
Continuity mistake: Bart's bedroom is on the opposite side of the stairs, with his window facing out to the backyard, but after his prayer his bedroom window is facing The Front of the house. Additionally, the style of his window changes as well, going from two horizontal sliding panes with no muntins, to a vertical sliding window with two muntins when Marge pulls the curtain back, then to a having only one muntin when Bart opens his window.
Continuity mistake: Near the start, when Homer is going through the medicine cabinet and we see various items. He takes out various hair growth products, and then when we see what's left, the floss has vanished. (00:01:10 - 00:02:20)
Continuity mistake: In the full view of Mr Burns' office when he is talking to Homer towards the end of the episode, there is only one fountain pen holder on the desk, but when Mr Burns tells Homer to leave after giving him his old job back, there are now two holders on the desk.
Continuity mistake: When Mr Burns tells Homer that he is only eighty-one in the meeting in his office towards the end of the episode, there is a fountain pen holder next to his arm on the desk, but when the camera is behind Mr Burns' chair in the next shot, the fountain pen holder has gone.
Continuity mistake: When Homer sobs after Bart dropped his bottle of Dimoxinil on the carpet in the bedroom, he drops the empty bottle next to the remains of the contents. When Homer is looking at Marge in the next shot, the bottle has disappeared.
Continuity mistake: After they say their goodbyes at the power plant, Karl asks Homer if he brought an umbrella and you can see that Homer is standing behind the doorway, but in the next shot he is now standing in the doorway.
Continuity mistake: When Homer opens the doors to the Executive Washroom, there is a sign on both doors, "Executive" on the left door and "Washroom" on the right door. When we see Homer walking with Karl and Smithers, the "Washroom" sign on the right door has gone.
Continuity mistake: When Homer runs out of the house with his new head of hair, there is only one doormat by The Front door. But in an overhead shot of Homer lying on The Front lawn surrounded by the children, a green doormat is now under the door.
Continuity mistake: When Homer parks his car outside Jake's Unisex Hair Palace, the doormat by The Front door entrance is light green but changes to dark green in the next shot.
Continuity mistake: When Homer is looking through the coat rack at the Royal Majesty, the coats he is looking through are coloured blue and red, but in the next shot they are now green and black.
Continuity mistake: When Homer runs out of the house with his new head of hair, there is a green mat on The Front doorstep. When the delivery man with the flowers is singing to Marge a little later on, the green mat is nowhere to be seen.
Continuity mistake: At the power plant's board meeting, look at Homer and you can see there is a piece of brown paper in front of him on the table, but when the camera is behind Mr. Burns, the paper in front of Homer disappears.
Continuity mistake: When Homer runs towards Moe's Tavern with his new head of hair, he looks into the window and you can see there is an empty beer bottle on the window sill next to him. When the camera changes to inside the Tavern in the next shot, the beer bottle has gone.
Continuity mistake: When the doctor (in disguise) gives Homer a wrapped-up present in the alleyway, they are standing next to a lorry and underneath the lorry there is some rubbish. But in an overview of the lorry in the next shot, the rubbish has disappeared.
Continuity mistake: When Marge comes out of the kitchen at the beginning of the episode, there are three ice cream sundaes on the tray she is holding. When Homer says "Hitler!", we cut back to Marge and there is now only one sundae on the tray.
Continuity mistake: During the dinner scene at the beginning of the episode, Homer is eating a chicken leg. When Bart says "Hitler", we cut back to Homer and the chicken leg he was holding has disappeared.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.