Continuity mistake: Stewie forces Lois to breastfeed him, and she undoes her shirt. As Brian and Lois argue about who is going to test her milk, Cleveland barges in and is shot. When Lois jumps up, her shirt is buttoned again, with no time for her to do it.
Continuity mistake: When we first see the English guy in his car, his crates of goods are stacked askew in the back seat. After Peter's crew shoot the car several times and the car is half-wrecked, the boxes are suddenly neatly packed into the seats. Moments later, we see the boxes piled randomly again. This change happens a couple more times before the scene is over.
Plot hole: Brian bets Stewie about being at high school for a week. However, this was before Peter's stroke, and before the fire at McBurgertown. It would take at least a few weeks for McBurgertown was rebuilt, then Peter had his stroke, and then Lois tells Chris Peter's stroke was 3 months ago. After this scene, Stewie tells Brian he has lost the bet. However, the bet would only last one week.
Continuity mistake: Meg comes in the kitchen and Peter pulls out her chair for her. Next shot of Meg shows a plate of food appear out of nowhere. Peter, Lois and Chris had a plate in front of them and there was no plate in front of Meg at any time. There was no other food in sight on the counter or stove either. (00:15:00)