Continuity mistake: The location of the comet in the sky changes direction at several points. Whilst it's apparent size and altitude will of course change, the direction it is coming from cannot. As an example, it is seen looming over the power plant towers, but when Ned is on the hill, it's no longer there.
Revealing mistake: When everyone is in Ned's shelter, the woman in the top left hand corner with brown hair and brown skin briefly has 2 pupils in each eye.
Continuity mistake: When Homer is driving home in a bad mood (just before he gets stopped by Chief Wiggum), you can see that there is a pattern on the side of the car. In a next shot when Wiggum is walking alongside the car there is no pattern.
Continuity mistake: Just before Homer (dressed as Krusty) is picked up by Officer Wiggum, his car is brightly painted and has wobbly clown wheels. When he pulls over it's back to the ordinary dented purple car he usually drives.
Continuity mistake: In the last scene when Homer is about to attempt the loop trick, it is seen several times that the Mafia guys are not standing in a straight line. In all shots they are except the one where Homer fails, and then says "Ta da,". The Mafia are shown head to head in a straight line.
Continuity mistake: When Homer arrives at the Van Houten house for Milhouse's party, Janey is among those at the entrance and she appears with yellow skin twice.
Continuity mistake: When Chief Wiggum pulls Homer over for speeding, all the clown decorations on his car have disappeared.
Continuity mistake: When Bart and Lisa are looking at the globe, Bart points out Argentina and 'Ran McNally.' 1) Next time you see the globe, it is showing Africa and Asia 2) Asia is shown incorrectly and 3) The equator has disappeared.
Continuity mistake: When Homer is threatening to boot the Prime Minister, he is holding him still with his left arm. When the shot goes to behind Homer, he has his right arm on the Prime Minister's shoulder. When the shot cuts back to a direct view of Homer, his right arm isn't touching the PM.
Continuity mistake: Two guards take down and eat the embassy flag. But when the Simpsons look down at the frogs at the embassy, the flag is still up on the pole.
Continuity mistake: When Bart is trying to get the toilet water to flow the other way, the toilet can't refill that quickly with that number of flushes.
Continuity mistake: When Bart is trying to make the toilet water flow the other way, in one of the flushes the toilet begins to dispense water before Bart pulls the chain.
Continuity mistake: Bart and Homer escape from the court by jumping out of a window, however in the next shot they are running away from the door as if they escaped via the doors.
Factual error: The Suburb of Wooloomooloo where the chase starts is in Sydney, and the Simpson family are chased all the way to the American Embassy which is in Canberra, a distance of at least 150 kilometres. That's some impressive running, especially for Homer.
Character mistake: Burkina Faso is listed as being among the Southern Hemisphere locations Bart called when Homer is looking over the phone bill; since Burkina Faso is completely within the Northern Hemisphere, it would have made no sense for Bart to call there.
Suggested correction: It may not make sense, but Bart isn't exactly the sharpest tool in the shed. In this same episode, he looked at his globe and thought Rand McNally was a country and was convinced by Lisa that the citizens there wear hats on their feet and that hamburgers eat people. Additionally, he could have just decided to prank call someone there if for no other reason than he thought the name of the country was funny.
Entirely possible, but since Bart had a globe right there to refer to, even someone with his limited geographical knowledge would have been able to tell that Burkina Faso is in the Northern hemisphere, unlike the other locations he did call as depicted in the montage (Antarctica, Argentina, unspecified South American nation, etc).
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Marge says, "I wish you wouldn't put Homer down like that.", Patty and Selma's dresses swap colour between shots.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When one of Marge's sisters says, "He blew all your savings on jack o'lanterns.", one of the armrests on the sofa is black for some reason.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer for the second time throws out Patty and Selma, the knocker just stays in the same place as if the door hasn't opened at all. (It looks like it is floating in mid-air).
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer tries to tell Marge how he did in the test, Selma and Patty are holding their cigarettes. In the next shot, the cigarettes are in their mouths.