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.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer is walking upstairs after kicking Patty and Selma out for the second time, the wall that Homer was approaching is a darker colour than it usually is, and Homer walked up the stairs slowly. But a second later he closed a door, indicating that he went into a room. Are we really to believe that he could go very quickly from the stairs to a room in a matter of seconds?
Homer vs. Patty and Selma - S6-E17
Continuity mistake: At the beginning of the episode, there is a drunk wearing glasses. He disappears in the next shot onwards.
Homer vs. Patty and Selma - S6-E17
Other mistake: When Homer burns a dollar bill, he turns his cigar around 180 degrees. If you look carefully, the smoke soon comes from the different side than it did earlier.
Homer vs. Patty and Selma - S6-E17
Revealing mistake: While the Simpsons are having dinner, the top portion of the chair Homer is sitting on disappears when he tilts the chair back.
Continuity mistake: When Wolfcastle says that 'Jay Sherman insulted him, now he will die', for a few shots the shadows are on the floor before they magically disappear. Also, the shadow of the gun does not match the real gun.