Plot hole: They're in the Clam complaining that they can't drink when they make the revelation that Brian can because he's technically 56. But Quagmire should be able to drink, as in a much earlier episode, he's revealed to be over 60.
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: 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.
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: 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: 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)
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)
Factual error: In the very beginning of Perfect Castaway, when Peter is talking to his workers and telling them he's going to have to "put them down", he pulls out a shotgun and four shells. He puts two shells in each barrel, but then continues to shoot 5 times when they jump in the water. First of all the shotgun is a double-barreled, break action type shotgun, so Peter should only have been able to put two shells in it. Second of all, even if he could put two shells in each barrel, he would only be able to fire it four times.