A Very Special Family Guy Freakin' Christmas - S3-E16
Continuity mistake: The wreath on the inside of the door changes from small to big. Notice when Peter goes outside to get a tree. Its bigger when he comes back inside the house.
A Very Special Family Guy Freakin' Christmas - S3-E16
Factual error: Brian touches the oven handle and gets burned. Not possible. Oven door handles do not get hot.
A Very Special Family Guy Freakin' Christmas - S3-E16
Factual error: A turkey does not burn and smoke 30 seconds after the oven timer goes off.

Continuity mistake: Lois and Meg take the red car for their vacation at the spa, but while they are gone, Peter is seen driving it a few times. (00:08:00)

From Method to Madness - S3-E18
Continuity mistake: While Stewie and Olivia are performing, Olivia is wearing a light purple dress. After the performance, when Stewie and Olivia are sitting on the piano talking to their teacher, Olivia's dress and hair bow changes from purple to blue in between shots. She is also wearing dark red lipstick instead of none at all.

Brian Does Hollywood (2) - S3-E2
Continuity mistake: As Peter and Lois take Stewie to the hotel, as we first see Peter, he has on a blue suit. The next scene we see him, he has on a black suit. Then, as they get called in the room, he has his usual on: green pants and a white shirt. (00:06:05)
Family Guy Viewer Mail #1 - S3-E21
Continuity mistake: When Lois is saying "We each seem to have acquired superpowers.", her size in relation to the chair in front of her changes between shots.

Continuity mistake: When Peter is calling for people to fight Lois, he is standing next to a sign that says "Fight the ass kicking housewife" and has metal rings at the top. When it moves to a closer shot, a hyphen has appeared between "ass" and "kicking". Then, after the space where the commercial break would have been, the sign now says "$10.00" and there are no metal rings. Finally, in the next shot, the sign says "Fight the..." and has metal rings on top. (00:06:55)
Family Guy Viewer Mail #1 - S3-E21
Continuity mistake: When the 'Knight' and the 'Ghost' bump into each other in the corridor, the armour and bedsheet fall on the floor, but in the next shot, the armour and bedsheet are gone. (00:18:40)
From Method to Madness - S3-E18
Revealing mistake: After the fight between Stewie and Olivia at the concert hall (followed by their breakup), Simon tells Stewie that the act without Olivia is "over" as he turns to walk off the screen. However, before Simon is even partially out of the shot, he completely disappears. (00:18:45)

A Very Special Family Guy Freakin' Christmas - S3-E16
Other mistake: When Quagmire is sticking his body out of the car door and yelling "Whooooooa! Whoooooooa!", look at the person in the back seat. It certainly isn't Joe, who was there in the previous shot, in fact it looks like another Quagmire. (00:05:30)
Suggested correction: That most certainly is Joe. It does not look like Quagmire at all.
While it's hard to call the face another Quagmire, the person in the back is wearing a Santa hat and same color/style coat as Quagmire. Joe was wearing a grey knit cap and different color/style coat. The person in the back also has black hair like Quagmire and not the brown hair Joe has.

Family Guy Viewer Mail #1 - S3-E21
Continuity mistake: When Lois picks up the fridge there is nothing stuck to the fridge but when she puts it down there is a note stuck to it. (00:09:40)

Mr. Griffin Goes to Washington - S3-E3
Continuity mistake: In the scene where Peter is at the baseball game, Stewie is sitting next to a boy he calls "Opie." The camera then cuts away to a clip. When the camera cuts back, "Opie" is gone and a grown man is now sitting next to Stewie. (00:02:55)
Stuck Together, Torn Apart - S3-E19
Continuity mistake: In this episode, Mort Goldman shows Peter a dating video he made, saying it's how he and his wife met. He is an adult in the video, yet in an earlier episode 'The Kiss Seen Round The World', Mort's wife tells the Griffins that she met him when they were just 14.
Family Guy Viewer Mail #1 - S3-E21
Continuity mistake: During the Scooby Doo send-up, there are red doors all along the corridor, but when Peter is talking about Istanbul, the red doors are gone. (00:18:35)

Continuity mistake: At the bottom of the stairs there is a picture of Peter and Lois, and the song "So Long, Farwell" starts. The kids start singing and you can see in the backround the picture is gone then comes back when the kids are going back up the stairs. Not only that, look closely at the picture of Stewie, you will see it has grown. (00:04:20)

Continuity mistake: When the family is in the traffic jam there's a shot from the front of the car, and in the next shot from the backseat of the car, Peter's face (glasses and part of nose) is reflected in the rear view mirror. However, there's no rear view mirror in the first front shot or shots following backseat shot.
Other mistake: The 'KISS' logo above Kiss's stage isn't actually held up by anything.
Audio problem: In the scene where Quagmire is bidding on the prostitutes panties, the auctioneer says that she had 9 STDs, but the closed captions have him saying, "She had 12 STDs." (00:03:20)

Continuity mistake: When Peter is pretending to be a man-eating tree, there is more of a shadow on the tree in the first shot than in the shot right after he spits out 'Dan Rather'. (00:05:50)