Other mistake: When Quagmire is sticking his body out of the car door and yelling "Whooooooa! Whoooooooa!", look at the person in the back seat. It certainly isn't Joe, who was there in the previous shot, in fact it looks like another Quagmire.
Continuity mistake: Brian gets the fur on his hands burned off by the kitchen fire, but when Lois goes crazy and goes into the living room, the rest follow her and the screen zooms out. When that happens Brian's fur is back on his hands.