Continuity mistake: Just before Peter enters the tunnel in his new car, the white line in the middle of the road is blotchy and not continuous. When the shot changes to Peter's POV, the line has completely disappeared. The next shot which shows the car side on, there is now a straight white line on the road.
Continuity mistake: While the Griffin family are at the Heimlich maneuver class, there is a scene where Stewie is talking to a doll and putting his clothes on. You can see that he has no shoes on but when he sticks his feet through the pant leg holes, shoes suddenly come out of the pants and he has his shoes on.
Trivia: In the episode "Blue Harvest, part 1," Peter narrates a telling of Star Wars from his point of view. When Chris is walking through the bar, we see Bender from Futurama, Coach John McGuirk from "Home Movies," The Evil Monkey from Family Guy and The Alien from American Dad sitting in the background talking to people.
Continuity mistake: Stewie tries to get his mind control device back from the kitchen. The cupboard door is open when he falls. In the very next shot, Lois turns the light on in the kitchen, and we see the door has closed without anyone touching it. It is open again after that.
Continuity mistake: While Stewie and Olivia are performing, Olivia is wearing a light purple dress. After the performance, when Stewie and Olivia are sitting on the piano talking to their teacher, Olivia's dress changes from purple to blue in between shots. She is also wearing dark red lipstick instead of none at all.
Continuity mistake: In the scene where Stewie is eating chocolate cake, he shoves his head in it and covers himself in cake. However when Peter walks in after having liposuction, all the cake has disappeared and Stewie is now completely clean. The bowl of grapes on the table is also gone.
Continuity mistake: After Lois accuses Stewie of peeing on the carpet, he asks her to bend down and slaps her with a glove. The glove remains in his hand in that cut, is still there when there is a wide shot of Peter, Stewie, Lois and Brian (you can just see it next to his trousers in his hand), but when it cuts back to Stewie and he starts on about "the outrages" etc, it is gone (the cut is instant, no time for him to put it back in his pocket). A common error, this one just struck me as strange, because the sandwich Stewie threw at Lois is there the entire scene.
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: At the bottom of the stairs there is a picture of Peter and Lois, and the song "So Long, Farwell" starts. The kids start singing and you can see in the backround the picture is gone then comes back when the kids are going back up the stairs.