Continuity mistake: In the episode "The Cleveland-Loretta Quagmire" 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: 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: 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.