Continuity mistake: Level 12 "Grand Theft Scratchy" cutscene: When Marge tells Poochie that even he isn't "extreme enough to resist the power of a stay-at-home mom, with too much time on her hands, " Poochie is wearing two bracelets, but next shot both bracelets have vanished, then continues to reappear (even within the same shot) and disappear again.
Other mistake: Level 5 "Mob Rules" cutscene: After Lisa gives Marge the manual and explains Marge's superpower to her, when Marge shouts, "Okay, let's stop that video game," Lisa's moving head was not properly edited by the layout artists, note that Lisa's head and neck are disconnected from her body, which is a bit creepy looking as she moves her head.
Continuity mistake: Level 14 "Big Super Happy Fun Fun Game" cutscene: When Milhouse hands over the keycard to Homer, he's holding it out upside-down, but in the next shot the keycard is rightside-up while he's still holding it out to Homer, but it's upside-down again when Homer takes it.
Continuity mistake: Level 15 "Five Characters in Search of an Author" cutscene: When Marge and her family walk over to Matt Groening, who's lying on the floor, we see that Marge has nothing on her back, but when Matt thanks Marge for saving him the empty baby carrier is now on Marge's back, though it vanishes again when Matt kneels in front of Lisa. As an aside, the baby carrier has two shoulder straps and a waist strap, but after Matt's escape when the carrier reappears on Marge the shoulder straps are gone, so it's pretty bizarre that Maggie could stay put in it.
Continuity mistake: Bargain Bin: When the mothership starts firing at the Simpsons, Homer drops the clipboard and pencil he was holding and it lands on the ground. Two shots after, the clipboard and pencil have disappeared. It couldn't have been out-of-frame because when it lands on the ground, it is in line with the path leading to the house, and the area surrounding the path is shown two shots after.
Continuity mistake: Game Over: When Lisa runs outside, Homer and Marge walk up to the door to tell her it's not safe. The hallway behind appears brightly lit in this shot. It then cuts to Lisa telling them her plan and when it cuts back to Homer and Marge, the hallway behind them is much more dimly lit.
Continuity mistake: Enter the Cheatrix: When Bart and Lisa walk up to Professor Frink whilst he is climbing down the ladder, the machine next to them has a couple of dials on them. Around these dials are a series of small lines (presumably a way of measuring different gauges). When the shot cuts to focus on Bart and Lisa, these lines around the dials have disappeared. A small arrow attached to the dials also disappears.
Character mistake: Game Over: In the flashback of God playing the Simpsons Game, there is a newspaper article on the wall with the headline "MAN ON MOON." Naturally, there will be spaces in between each of the words, but there are also spaces in between some of the letters in the word MOON; there is a space in between the M and first O, and a space in between the first and second O that shouldn't be there.