Continuity mistake: When we first see Kate and her parents at the restaurant there are only 2 empty chairs. Stewie then sits in the chair next to Kate. After Kate's parents ask what happened, we see a chair in between Stewie and Kate, but you can also see the edge of third empty chair. A plate and the wine filled glass also move.
Character mistake: After Stewie and Brian go to tell the past versions of themselves not to tell 1999 Brian about 9/11, Stewie then finds out that Brian then told 1999 Brian to write the Harry Potter novels. This would have been impossible because the first Harry Potter novel was written in 1997, 2 years before the time period Stewie and Brian arrive in.
Continuity mistake: Near the end of the episode, Joe and Quagmire are shown sitting at a booth inside the bar with Joe pulled up to the corner of the booth. As Peter apologizes to them, Joe is no longer seen next to him. As Peter takes Quagmire's check, a part of Joe is seen sitting in the next booth. In the shot after, he disappears again for the rest of the scene.
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Continuity mistake: In the scene with the multiple versions of Stewie and Brian come back to 1999, one Peter is with one of them. When Stewie asks everyone to vote between 9/11, Peter is standing in the foreground, but disappears when one of the Stewies says Brian had his throat slit.