The face masks in the medicine woman's shelter and the totem poles are not part of Inuit culture. They belong to the Haida Indian tribe who reside much further South down the British Columbia West Coast and the South East area of Alaska in the temperate rain forests.
At the start of the movie the church is shown set back from the street (correctly), in later scenes it is shown right by the road, next door to Moe's Tavern. On the DVD commentary, the film makers decided it would make more sense to have the church next to the bar since there is a scene where the alcoholics in the bar go pray and the worshippers of the church go drink.
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).
In the Motel scene many times, you can see that the lock chain slot on the door doesn't have the circle where you put the chain through. It has it in a few shots but than in others it is a straight rectangle.
When they flee the house and jump into the car, the house is on fire, even when Marge runs back into the house to save her and Homer's wedding video, it is on fire. When the townspeople carry the car to the backyard, the house is not on fire.
When Russ Cargil is speaking to the town of Springfield on the big screen, on the top left hand corner you can see the Simpsons house with the dome turning on an angle cutting half way through the yard, but in other shots it is perfectly straight right at the back of the yard.
When Marge and Bart are inside the gas station store while Homer puts gas in the pickup truck, Bart places a buzz cola on the counter next to the beef jerky. When Bart aims his sling-shot to shoot the hot dog off Homers' hand, the buzz cola is now near the tip jar. After he shoots the hot dog, the buzz cola is gone.
In the scene with Cargill is in the Oval Office, the portraits change. At first, the pictures are of Ronald Reagan and assumably, Maria Shriver. In the next shot, the portraits have been replaced by a mountain landscape scene.
When Lisa is visiting the neighborhood's houses with the petition to stop dumping in Lake Springfield, she comes to Milhouse' house, his lawn is empty but in the next scene there is a large rock in the middle of his lawn.
During the Church scene when Flanders is confessing to the immodest sense of pride; Chief Wiggum is clearly sitting behind Flanders. However, when Grandpa Simpson is doing his monologue of warning, Chief Wiggum seen on the other side of the church.
When Russ Cargil is talking to Springfield for the first time, he says that he trapped them like carrots. You see Moe standing next to Lenny and Carl, who then nod their heads at each other. 6 seconds later, Moe is standing alone at the back of the crowd.
When the dome is being placed over the town you see a clip of the dome settling down crushing a fence. In the next scene you see the dome a good 25 feet in the air awhile a guy is taking his time debating whether or not to stay in the dome or to leave.
Toward the end of the movie, Bart, Lisa, Marge and Maggie are prisoners in the back of the EPA's van, Lisa is seen (and heard) playing her saxophone. However, in the beginning of the movie, all 5 Simpsons escape the dome totally empty handed.
When the dome is being lowered and the guy is thinking whether to stay in or leave, it seems about a feet thick at least, However when Lisa and Colin place their hands on the opposite ends of the dome it seems only about an inch thick.
In the assembly scene, Kent Brockman is seen in the first row, he is wearing a white t-shirt, but when the audience spits out the lake water that they drink, you can see Kent to the far left of the close up wearing a red coat.
In the scene of Bart's Avalanche, when Homer is buried the second time and he comes out, his hair is ruffled, when the shot changes to Bart and Lisa, his hair is back to normal, this happens a couple of times.
When Homer and Bart are at Krusty Burger, while Krusty is filming his commercial, the pig runs to Homer in fear of being slaughtered. While Homer's looking down at the pig, Bart is shown to be wearing his regular blue shorts instead of the jeans that Flanders gave him.
When the Simpsons are in Bart's tree house and it is being pulled down by a school bus, we see Grampa Simpson take aim at them with a shotgun that obviously has two barrels, but he cocks it by pumping it. A double barreled shotgun is cocked by pulling the hammer back.
The medicine woman and Homer don't introduce themselves - since Homer is unconscious when we first see her - yet when she attempts to revive him she calls out his full name. However, as the medicine woman is a mystic of some sort, she would not have needed to ask his name, as she may have predicted this, read his mind while he slept - or even looked at his drivers license.
Hans Moleman is present when Homer dumps the silo in the lake, but nobody finds out it was him until it's discovered. A running gag on the show is that Hans Moleman is shown in situations where he could possibly die, which could be the case here.
When Homer goes to the fair, he uses the last $10 that the family has to win a truck. In the next scene at a gas station, Homer is filling up gas, and Marge is planning to purchase beef jerky. However, just because it's the next scene doesn't mean it happened immediately afterward. They could have won some other contest, or tricked someone, or there could have even been some cash in the truck.
During the scene when Moe dumps the truck full of empty beer bottles into Lake Springfield, look closely at Moe in the truck. As his head turns away, there is no animation of his head turning and it simply "jumps" to him looking forward.