Revealing mistake: During the scene when the people at the pool think Chris is a car sitting on the diving board, just before Lois moves out of the shot before the scene changes, her lips disappear for a split second. It's really fast but still easy to notice even without pausing or slow motion.
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.
Continuity mistake: When everyone is in the dining room at the dinner table, the order of where everyone sits changes between shots. In all moments where it shows everyone sitting, the order is Priscilla, Derek, Jillian, Mort, Muriel, and Carl. But in one shot, the order is Priscilla, Derek, Jillian, Muriel, Mort, Carl.
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 episode where Brian and Lois get married, Lois confronts Brian after cheating with Peter back at the house. Stewie is playing with a SIMON SAYS game. Look at the SIMON SAYS when he is playing it (up close), after he is done (the close up shot ends), look at the colors again on the SIMON SAYS, they change.
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: 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: In the flashback when Peter fights Ernie the Giant Chicken, Peter gets knocked off the top of an eighteen wheeler and grabs the second rung at the bottom of the truck's ladder. But when the truck driver sees the pair in his side view mirror, Peter is hanging off the top of the ladder.
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.