Factual error: In all the scenes where Peter wrecks Cleveland's house and Cleveland is in the bath, the tub always slides easily out of the house with Cleveland in it and onto the ground. There are no pipes or any kind of plumbing visible on the bathroom floor where the tub should have been connected.
Continuity mistake: The age difference between Chris, Meg and Stewie keeps changing throughout the series. At the beginning of the series, Chris is 13, Meg is 15 and Stewie is 1 (he is after S1 E3 Chitty Chitty Death Bang). In series 4, Chris then goes to high school so he must be 14 by that time. It isn't referenced that Meg has aged between series 1 and series 5 until S5 E10 Peter's Two Dads where she turns 17, so she must have turned 16 during the past five seasons. Despite Meg having aged two years throughout the series, Chris remains having only aged one year since S4 (Age 14 referenced in S9 E13 Trading Places). Then in S10 E10 Meg & Quagmire, Meg then turns 18, and still Chris hasn't aged. Also, Stewie remains one year old after all of Chris and Meg's birthdays. If it were consistent, Meg would be now 18, Chris would now be 16 (not 14) and Stewie would now be 4 (not 1).
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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.