When Peter visits the cardinals' hotel room, we see a man with a purple "POPE-APALOOZA" jacket on a cell phone. In the first shot "POPE-APALOOZA" is written on two lines, but in the next, it is written on one.
During the last scene when Peter and his family are watching TV. The night sky can be seen through the window. When Peter and his family fly away in the pod, it is daytime outside.
The bite on stewie's sandwich changes from the middle to the side.
When Peter's mom is knocking on the front door the doorknob is on the wrong side.
When Peter is at the PawSox game with his father he suggests getting a Fenway Frank. They are not sold at McCoy Stadium, where the PawSox play.
While reading the Bible Stewie mentions that he loves the part about lions eating Christians. The Bible has no mention of anything like that.
It is not possible to open any doors on an airliner at cruising altitude.