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.
Audio problem: After Lois goes insane and jumps out the window, she insults Frosty the Snowman, who then goes up to her to demand an apology. Lois then takes out a match and uses Frosty's nose to light it. Frosty recoils, holding his nose and saying "Ow, ow, what the-" but it cuts to a shot of Lois grabbing a bottle of beer from a hobo as Frosty is saying "What the" and it shows him standing perfectly straight, with his mouth not moving at all.
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.