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 were Venice, with the sea, the lagoon, and the canals.
Continuity mistake: When Bertram sneaks into Stewie's bedroom, he tiptoes past Stewie, who is sleeping. But in the next close-up of Bertram, the shot pulls back and pans the room so we see Stewie's crib is empty. But in the next shot, Stewie is still sleeping, and then he wakes up. (00:10:25)
Continuity mistake: When Bertram climbs through the window into Stewie's bedroom, just as he tiptoes past a sleeping Stewie, the lightswitch on the wall is in the up position and the room is dark, but two shots later Stewie wakes up and now the lightswitch is in the down position so Stewie flips it up, then the light turns on. (00:10:20)