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, they could have obtained more cash in between scenes.
When Doctor Hibbert asks Mister Burns for power supply for the hospitals, Mister Burns writes it down using his right hand but it is an unchangeable tenet of the The Simpsons that Mister Burns is left-handed.
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.
At the start of the movie the church is shown set back from the street (as it is in The Simpsons), 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 worshipers of the church go drink. But they either forgot or were unable to go back and fix the other scene to make it consistent.
When the dome is being lowered and the guy is thinking whether to stay in or leave, it seems about a foot 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 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.
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.
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).
When Russ Cargill is speaking to the town of Springfield on the big screen, on the top left hand corner you can see the Simpson 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.
When Cargill is in the Oval Office, the portraits change. At first, the pictures are of Ronald Reagan and Maria Shriver. In the next shot, the portraits have been replaced by a mountain landscape scene.
When Lisa is visiting the neighborhood houses with the petition to stop dumping in Lake Springfield, she comes to Milhouse's 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 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 Russ Cargill 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.
When Homer is riding the wrecking ball, he first bumps into a giant metal statue then into a fork on a bill board. However, in the next shot, he is bouncing between the rock and the "Hard Place" and neither the statue nor the fork are visible.
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.
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.
Marge, Bart, Lisa and Maggie Simpson take a passenger train from Alaska to Seattle, WA. (The exact same train seen in Alaska is shown arriving in Seattle). There is no railroad link between Alaska and any other US state.
Hans Moleman is present when Homer dumps the silo in the lake, but nobody finds out it was Homer until the silo is discovered. But Hans doesn't have good eyesight and isn't very quick on the uptake. There is also a The Simpsons running gag where in several episodes Hans disappears and is presumed dead, only to turn up alive in a later episode, so this could be his disappearance for the course of the movie.
As the Simpsons probably didn't have their passports, they shouldn't have been able to cross the border to Canada, and again when they reached Alaska. Even if they had they would have been caught and arrested because they were fugitives.
When Moe dumps the truckload 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.
When Homer is first seen climbing the dome with super glue on his hands the camera pulls out to show virtually the entire dome, yet there is no sign of the helicopter dangling the bomb through the hole, although a subsequent shot shows it only a few feet above the top of the dome. Nor is there any sign of the bomb itself or the rope that supports it.
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. But Homer was probably carrying his driver's license which she read.