Factual error: You cannot get paternity test results back in one day. It takes 3 to 5 days or even weeks depending on the lab.
Continuity mistake: When Joe eats ice-cream on a mini batting helmet during the football match, some ice-cream is visible fallen on the ground just before the drink seller comes. In the next shot it disappears. (00:02:40 - 00:03:01)
Continuity mistake: Lois and Brian go outside and celebrate Peters dads death. Behind them you see the trash cans. They come back in and sit down and the trash cans have vanished. (00:12:33 - 00:12:54)
Ratings Guy - S11-E2
Factual error: Mayor West destroys all of Peters Neilsen Rating TV boxes by blowing them to pieces. At the end of the episode we see Herbert with the boxes all "taped" up and he's now using them. Not possible.
Other mistake: A bank wouldn't lock someone in the vault all night. Employees make sure customers have left before locking up for the day.
Continuity mistake: After getting the uranium, Stewie places it in the time pad and then puts the pad in his jacket pocket. After being confronted by Hitler who promises to spare them if they sing a musical number, Mort interrupts them, and it's seen that he is now standing on the time pad.
Factual error: The family stays briefly in a British apartment, however the plug sockets displayed are US standard, not UK.

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)

The Cleveland-Loretta Quagmire - S4-E5
Continuity mistake: While the Griffin family are at the Heimlich maneuver class, there is a scene where Stewie is talking to a doll and putting his clothes on. You can see that he has no shoes on but when he sticks his feet through the pant leg holes, shoes suddenly come out of the pants and he has his shoes on. (00:04:10)

And Then There Were Fewer - S9-E1
Continuity mistake: When everyone is in the dining room at the dinner table, the order of where everyone sits changes between shots. In all moments where it shows everyone sitting, the order is Priscilla, Derek, Jillian, Mort, Muriel, and Carl. But in one shot, the order is Priscilla, Derek, Jillian, Muriel, Mort, Carl.

Continuity mistake: Brian's newspaper's name changes from "Daily Informant" to "Daily Tim...". The newspaper also turns upside down between the two shots. (00:11:15)

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.
Continuity mistake: When Peter and the chicken are fighting, everything in the road vanishes instantly.
Plot hole: Stewie gets out of the car seat and goes back to bed, leaving the blanket at the bottom of the seat. When they get to New York, Lois goes to get him out and realises he's gone. But when they started the trip the blanket was covering the entire seat to make it look like Stewie was still in it. So who ever "covered" him up knew he wasn't in the seat before they set off. (00:13:45)

Continuity mistake: In the flashback when Peter fights Ernie the Giant Chicken, Peter gets knocked off the top of an eighteen wheeler and grabs the second rung at the bottom of the truck's ladder. But when the truck driver sees the pair in his side view mirror, Peter is hanging off the top of the ladder. (00:02:00)

The Courtship of Stewie's Father - S4-E16
Continuity mistake: After "Herbert the Pervert" leaves the Griffins' house, the size of the couch in relation to Chris changes distinctly between shots.

Continuity mistake: Stewie tries to get his mind control device back from the kitchen. The cupboard door is open when he falls. In the very next shot, Lois turns the light on in the kitchen, and we see the door has closed without anyone touching it. It is open again after that. (00:09:50)
Continuity mistake: Stewie forces Lois to breastfeed him, and she undoes her shirt. As Brian and Lois argue about who is going to test her milk, Cleveland barges in and is shot. When Lois jumps up, her shirt is buttoned again, with no time for her to do it.

Continuity mistake: When Peter is testifying in court, the microphone on the witness stand disappears in the shots from the judge's point of view. (00:18:43)
Answer: Lacey Chabert was the actress who originally voiced Meg in early episodes. She left of her own accord due to being in school and other acting work; Seth MacFarlane has stated there was no tension with her leaving, but it makes for a handy joke for the show.
Jon Sandys