Continuity mistake: After Peter says goodbye to his family before his flight to Ireland, when it cuts to Stewie spying on Lois while she's doing the dishes, there's a calendar hanging on the wall beside the refrigerator and a paper hanging on the fridge, but when Stewie draws on the wall both the calendar and paper have vanished.
Continuity mistake: Peter goes to see his mom. She's drinking coffee and puts the cup down on the table to answer the door. In the next shot the cup disappears.
Continuity mistake: Lois and Brian go outside and celebrate Peters dads death. Behind them you see the trash cans. They come back in and sit down and the trash cans have vanished. (00:12:33 - 00:12:54)