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.
Continuity mistake: After Lois says, "When Meg and Chris turned one I missed everything," it flashes back to Lois writing 'happy birthday Meg' on the cake, and there's wallpaper border at the top of the walls, but when Peter asks her what she's doing in the kitchen the wallpaper border is gone. The paper cups that Lois filled with punch also vanish, and the rolling pin, board, etc. suddenly appear. (00:11:30)
Continuity mistake: When Brian and Stewie arrive in Leonardo's atelier we know that they are in Florence for two reasons: because of history and because we see Palazzo Vecchio (which is in Piazza della Signoria, in Florence) outside the window. Then when Stewie and Bertram are fighting with Leonardo's flying machine the city of Florence is wrongly represented as if it was Venice, with the see, the lagoon and the canals.
Continuity mistake: When Brian stops at the Marriott, he orders a Jack on the rocks. As he is ordering it, there is a woman in the background with a martini, then when the camera cuts to behind the counter when Brian receives the Jack on the rocks, the same woman has red wine instead of a martini.