Continuity mistake: After Steve accidentally jabs the wood burner into Stan's penis, he screams and a avalanche occurs. Then when Stan screams a second time due to putting the cream on his penis, the avalanche happens again but the same amount of snow is on the mountain even after a load already fell off it. (00:06:40 - 00:07:30)
Continuity mistake: When the avalanche happens the second time, all of the animals have snow on their backs. In the shot of all three of the animals, the snow has disappeared. (00:07:30)
Continuity mistake: Episode 1-10, "All About Steve": The boys are sitting at a table with a Star Trek poster on the wall. Stan walks in and the poster is gone. In a later shot it is back. (00:04:30)
Continuity mistake: At the convention when we first see Roger and Hayley, they pass a booth that says Costume contest registration. There is also a few people around, a poster and a movable wall. The very next shot is more of a close up of the two and the background has changed dramatically. There is now about 4-5 different stalls behind them and no sign of the previous one or the poster and wall.
Revealing mistake: When Stan comes home and starts talking to Francine, as Francine is saying "You're just having a mid-life crisis", there are three objects in the background that are cut in half and seem to be floating in the air. (00:02:10)
Revealing mistake: While Hayley is throwing up into the bin, you can hear the sound of it going into the bin. However, you can see nothing is actually going into the bin while she is doing it.
It's Good to Be the Queen - S1-E20
Continuity mistake: At the hotel, the dish with the strawberries is sitting alone on the round table. When Stan knocks it off, the table is now empty, but in the next shot, there's a phone and glass on the round table.
Chosen answer: It is just the decision of the creators to do so.
MasterOfAll