(at around 35 mins) 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 around 4 mins) At the start of the movie the church is shown set back from the street (as it is in The Simpsons (1989)), in later scenes (at around 27 mins) 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.
(at around 24 mins) When Homer dumps his silo of pig waste into Lake Springfield, he cuts the ropes with an axe, and dents the side of the car. The dent is gone in all subsequent frames.
(at around 40 mins) When Homer enters the hotel room, the door swings open even though the security chain was in place and all the family members were halfway across the room.
(at around 27 mins) 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. (at around 38 mins) However when Lisa and Colin place their hands on the opposite ends of the dome it seems only about an inch thick.
(at around 56 mins) 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.
(at around 41 mins) Homer pulls an orange "Get Out of Jail Free" Monopoly Community Chest card from his wallet. In an American Monopoly set, Community Chest cards are yellow. Chance cards are orange.
(at around 3 mins) Billy Jo Armstrong's arm tattoos are missing.
(at around 36 mins) 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.
Under federal U.S. regulations, anyone under the age of 18 is prohibited from operating machinery like the scissor lift Lisa uses at the town hall meeting.
(at around 23 mins) 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 (1989) 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.
The Simpsons leave the dome with nothing. However when Marge, Bart and Lisa are on the train and in the EPA van, Lisa has now got her sax. However, in Alaska they wear cold-weather clothing, which they also did not take with them, so during the clothes shopping trip they may also have bought Lisa a new saxophone (presumably with the $1,000 they received.)
Though Arnold Schwarzenegger is shown being the President of the United States, in actuality he wouldn't be eligible to hold the office, as the US Constitution requires the President to be a natural-born citizen. However, the Equal Opportunity to Govern Amendment (sometimes referred to as 'Arnold's Amendment'), which would allow foreign-born naturalised US citizens to run for President, was proposed in 2003 by Senator Orrin Hatch, so this film may be set in a universe where this amendment has passed.
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.
(at around 16 mins) When Bart is aiming his slingshot at Homer, you can clearly see there is no stone in it.
(at around 31 mins) When Homer and Marge go out and look for Maggie, Homer sees his reflection and thinks he's outside of the dome. Yet, Marge's reflection is not seen, even though Homer runs around her.
(at around 35 mins) When Marge went back to get one item from their burning house, she took their wedding tape. Homer and Marge had no wedding; they got married in a wedding chapel across the state line.
(at around 29 mins) When Russ Cargill appears on the dome over Springfield for the first time, watch the crowd on the bottom of the screen. One citizen's hair was not colored in and is transparent.
(at around 19 mins) 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.
(at around 3 mins) When Green Day's barge begins to sink, they all pull out violins. However, when they start to play, you hear a cello as well.
(at around 1h 2 mins) When Lisa is playing her saxophone in the van after the family has been picked up by the EPA, an alto saxophone is heard. But Lisa plays the baritone saxophone.
(at around 57 mins) 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.
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 Lenny calls Homer about free doughnuts Hans Moleman is in the background (in Lenny's scene) then Homer drives to the lake to dump the pig crap silo and he runs over Hans Moleman, But he was at the doughnut shop so he couldn't have gotten to the lake in time.
There are two cars driving behind the EPA truck containing Marge, Bart, Lisa and Maggie. But when Homer uses the bulldozer to try and break the family out the truck, the two cars behind the truck don't even realize for some strange reason that a bulldozer is trying to destroy the truck. There's no way they couldn't have not seen the bulldozer since they were just behind it.
The pig is forgotten about after the Simpsons escape the house.
Bleeding Gums Murphy can be seen in the Angry Mob scene, even though he supposedly died in the episode 'Round Springfield (1995).
(at around 46 mins) 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 (1989) that Mister Burns is left-handed.
In anticipation of their deaths, Flanders reminds Rod and Todd to call Jesus "Mr. Christ" when they meet him. A devoutly religious man like Ned would know that, according to the Gospels, "Christ" was not Jesus' surname, but a title bestowed upon him as the prophesied Messiah; by modern analogy, it would be akin to addressing Queen Elizabeth as "Mrs. Queen".