Audio problem: Just after Peter graduates from the Police Academy, he goes home to Lois and draws his gun in the kitchen, which gets Lois very excited. Every time Peter fires his revolver, you'll hear a soft, but distinctive clink briefly after each shot. This clink comes from shell casings hitting the floor, which revolvers make impossible. Revolvers are designed to eject expended shell casings only while its user is reloading, not after each shot is fired. Only semiautomatic firearms immediately eject expended cartridges immediately after having been fired. Unless I'm mistaken, the entire gunshot sound originally came from a 9mm semiautomatic pistol.
Continuity mistake: At the Little Miss Texas pageant, just as Lois finishes saying "It's what you do when you're in Texas", she and Stewie walk past a judge and a little girl. In a close-up of Stewie, the judge and little girl have suddenly become a plant. (00:15:25)
Continuity mistake: Peter says "Oh crap" as soon as he realises Ernie the Giant Chicken is looking at him in the window. When the camera pans over to Ernie, he is standing an inch away from the glass. It then cuts to a wide angle where Ernie jumps through the window, and he has instantly moved back a few inches. (00:07:00)