Continuity mistake: When the Simpsons are driving to Alaska, Homer puts the poster of Alaska on the window. Marge then removes the poster and we see the van is going out of control. In the next shot that shows them screaming, we can see they are driving totally normally judging by the view from the back window. (00:45:05)

Continuity mistake: The bottle of ink and quill on Mr. Burns' desk disappear for one shot. This happens when Apu, Chief Wiggum and Dr Hibbert are asking for some electricity. (00:46:05)
Continuity mistake: When Homer tells Lisa to clap in Alaska, there is some snow on his left ear that moves to the top of his head. (00:46:05)

Continuity mistake: When the family move to Alaska, the door to their cabin opens to the left (looking at it from the inside) when Homer escapes from Bart and Lisa's "avalanche". But later in the film it opens to the right (from the inside). (00:46:25 - 00:52:05)
Continuity mistake: The door to Homer's cabin in Alaska changes positions, from facing the street when he comes home from the bar to facing over a cliff when he decides to follow Marge and the kids back to Springfield. (00:46:25 - 00:52:45)
Continuity mistake: In Alaska, when Homer is holding the wood logs, the amount of logs changes from three to four between shots. (00:48:00)
Continuity mistake: Barney runs head first into the dome and slides down horizontally. Next shot he is stood up and is shoulder barging the dome. (00:48:10)

Continuity mistake: When Homer is forced into the house by Bart and Lisa's avalanche, it is broad daylight, but seconds later he is with Marge in the bedroom and it is dark outside. It is not snow surrounding the house, because the animals come in through the windows. (00:48:30)

Continuity mistake: The second time Russ Cargill spreads out the five options on the President's desk, the name bar with 'President Schwarzenegger' on it vanishes and reappears on the desk twice. The spread of the files also inverts between shots. (00:50:40)
Continuity mistake: Homer leaves Eski-Moe's with nothing in his hand. Then he grabs onto the back of a truck with still nothing in his hand. Homer lets go of the truck and zooms to the house and there's still nothing in his hand. But when he opens the door, there's suddenly a bouquet of flowers in his hand. (00:51:55)
Continuity mistake: At the start of the scene with the medicine woman, Homer is under a blanket. In the first shot, his entire body is under a fur blanket. But in the next shot of Homer, his arms are suddenly out of the fur blanket. (00:55:30)
Continuity mistake: When Homer returns to Springfield, there is full security around the Dome. However, when the bomb explodes there is no sign of any security whatsoever. (01:00:00 - 01:10:25)

Continuity mistake: When Homer is on the wrecking ball, he hits a fork on one side but in the next shot it vanishes. (01:01:00)

Continuity mistake: When Homer is dressed as General Marriot Suites he's wearing white gloves but after he punches the guard the gloves have vanished. (01:03:30)

Continuity mistake: After being held in the EPA truck, when Marge and the kids wake up at the Town Square - the remains of the courthouse with its lion statues are behind them. The buildings to the left of the courthouse change in following shots, such as while Cletus distracts Cargill, or when Homer's on the motorcycle and grabs the cowboy hat. (01:04:30)

Continuity mistake: When "Emperor" Moe appears in front of Marge, after she and the kids return, the two cartridge belts swung over Moe's shoulders switch from his left over the right, to his right over the left. (01:04:50)

Continuity mistake: When Homer is climbing the dome, there is a shot of the rope. No-one is climbing it, yet a few seconds before people were climbing the rope. (01:05:10)
Suggested correction: They didn't climb high enough to be visible. Homer was much higher than they were.

Continuity mistake: In the scene where everyone is climbing the rope to get on the top of the dome, Homer should already be at the top, but when the camera points to the top of the dome, he does not appear there. The next scene shows him back at the top of the dome again. (01:05:15)

Continuity mistake: When Homer kicks over the bomb, Comic Book Guy is seen seen behind him, with Carl, Cletus, and Krusty. In the next shot, Comic Book Guy is gone (appearing a few shots later at his comic book shop), and Barney is there instead. (01:08:45)