Continuity mistake: At the mall Stewie is wearing a pair of mustard color fingerless mittens, and the problem occurs while Stewie is sitting on Santa's lap. When Stewie first mentions plutonium and being a good boy, Stewie's hands show all of his fingers which means he's mittenless, but the color of his hands is the same color as his mittens. Then, when Santa tells Stewie to wrap it up, Stewie is wearing his mustard color mittens, then his mustard color fingers return again.
Continuity mistake: After the Robert Redford clip, when it cuts to the Griffins walking toward Doug's house, in this exterior shot (and a previous exterior shot) the front door is located between one window and the garage, but in the following interior shots there's a window on both the left and right side of the front door. (00:14:20)
Continuity mistake: While Lois is driving her family home from the mall, the animation process did not properly color Lois during the car ride. First, she's wearing white gloves, but in one shot both of her hands are bare on the steering wheel. Second, Lois is wearing a green coat and white scarf around her neck, but in the shot facing the town's tree through the windshield, her scarf/collar is red (her Santa hat has a red narrow tip with a white pom-pom).