When Peter first claims he's Jesus, Chris disappears from the couch between shots.
Stewie forces a rat to vomit on a customer's prime rib. In reality, rats are incapable of vomiting.
The doors to Peter's restaurant open inwards. This in violation of public buildings code where all doors must open outwards in case of fire and a fast moving panicked mob of people trying to exit.
Peter says he adopted 30 puppies. He's actually carrying 33.
Mort asks Lois for a crucifix, preferably one without the little guy on it. A crucifix is different from a standard cross because it has the figure of Christ on it. So, without the little guy, it would just be a Christian Cross and not a crucifix.