Factual error: In the park, Stewie and Brian are playing the "water pipes" like a xylophone. Trouble is, in order to get the tones they were playing, the glasses should have had different levels of water in them. If you look closely, all the glasses have the same level of water.
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Factual error: Brian is sitting on the couch smoking weed. Joe knocks on the door and Brian just waves the smoke from the air. Joe is there to give Brian a drug test and says nothing about smelling weed in the air. There's no possible way he didn't smell it! You can't just wave your hand and get rid of the smell.
Continuity mistake: Peter gets beat up and thrown in to a black limousine by hired thugs of Mr. Pewterschmidt. While in the car, notice that as Peter starts talking to Mr. Pewterschmidt that there is no cart of Diet Rites next to him. Next shot there is. Then the cart disappears as Mr. Pewterschmidt tells Peter what is on his mind.