Homer Badman - S6-E9
Character mistake: When Grandpa is putting up the American flag for Homer's public access show and Marge says the flag only has 49 stars, there are actually only 38: 8+7+8+7+8.
Character mistake: In the scene where the imposter Krusty is robbing the Kwik-e-mart, Krusty's hair is blueish green just like the real Krusty, but when Homer is describing the robber he says the the crook has red hair. This is so you have more clues on who the real impostor is. The imposter Krusty is really Sideshow-Bob who has red hair. (00:04:20 - 00:05:05)
The Last Of The Red Hat Mamas - S17-E7
Character mistake: When Homer finds Marge's folder, it reads "Heist Plan: Burns Manson" instead of "Mansion" as it should be.
Character mistake: When Homer discovers that the Leftorium is going out of business, there is a sign that says 'Coming Soon: Gum for Less' beside the store. Later on, though, Ned says the new store is becoming 'Libertarian Party Headquarters.' (00:15:50 - 00:19:15)
Suggested correction: The sign is just an advertising poster that's on a wall. It's not in front of the leftorium.
Sideshow Bob's Last Gleaming - S7-E9
Character mistake: Homer drinks 6 non-alcohol Duff at the air show, but is charged for 8.
They Saved Lisa's Brain - S10-E22
Character mistake: The plural form of ignoramus is ignoramuses, not ignorami. The word "ignoramus," a Latin verb-form meaning "we do not know," has no Latin plural-noun form. Therefore, when used as an English noun it correctly pluralizes as "ignoramuses." Someone as smart as Lisa should know this.
Character mistake: Lisa states that Pierre and Marie Curie both died of radiation poisoning. This is incorrect, as only Marie died of radiation poisoning while her husband Pierre was killed by a horse and cart. (00:08:30)
Homer's Barbershop Quartet - S5-E1
Character mistake: When Marge is making a model of Homer for Bart and Lisa, she makes him bald with his hair round the back of his head as we all know it, but at this point in the story Homer was not yet bald. (00:18:15)
Character mistake: When Bart fakes being sick, on his way to the infirmary he passes the door with a sign that reads "maintanence" but the proper spelling is "maintenance", and when Bart reaches the infirmary, the sign on the door reads "ineirmary." (00:07:30)
Who Shot Mr. Burns? (2) - S7-E1
Character mistake: Willie says he got arthritis from playing Space Invaders in 1977. However, Space Invaders didn't come out until 1978.
Character mistake: Moe says that no women have been to his bar since 1979, yet in "Flaming Moe's" he hires a female waitress. Also, in the episodes "New Kid on the Block" and "Homer the Vigilante," Ruth Powers appears in the bar, and orders a beer in the former episode while Marge visited the bar in "Bart Gets Hit By a Car."
Tree House of Horror X - S11-E4
Character mistake: When the Collector is putting Lucy Lawless into her plastic bag in his lair with the other celebrities, he refers to Tom Baker as "Doctor Who." As a sci-fi nerd, he would know the character's name is simply "The Doctor."
Character mistake: When Hugh proposes to Lisa using the electronic signage, he spells the word "honor" using the American English spelling. Hugh should have used "honour" as this part of the show was set in England, and Hugh is from England.
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).
Character mistake: When Martin Prince supposedly represents Finland's culture for their recreation of the U.N at the Model U.N. Club Martin's outfit is not in fact a Finnish national costume. The outfit he is wearing actually resembles a traditional Sámi outfit. The Sámi people are the indigenous people living in Northern Europe. The specific style of Martin's outfit has characteristics that are more typical to the Sámi on the Swedish side of Sápmi. (00:02:15)
Character mistake: Before their first performance, the director of "La Boheme" wishes Homer good luck. To anyone in professional theatre, doing so is the cardinal sin of theatrical superstition and is never done; the appropriate phrase is "break a leg."
Character mistake: When Maggie starts speaking Ogdenvillian, Marge says that it is her first word. But in the episode "Gump Roast", everyone, the Simpsons included, all watched a video of Maggie saying her first word. (00:17:35)
Another Simpson Clip Show - S6-E3
Character mistake: In the first scene, Marge says that it is 9:30pm, but after Homer's flashback, the clock next to Homer reads 11:50.
Character mistake: When Chief Wiggum shows up to arrest Nelson during the game at the end of the episode, Bart goes with Wiggum instead while pretending to be Nelson. Even a cop as incompetent as Chief Wiggum would not have mistaken Bart for Nelson since he'd had numerous dealings with both before this episode; Wiggum may not be particularly bright, but he knows who's who in Springfield.
Character mistake: When Mr. Burns and Smithers are walking through the morgue, the sign on the wall is incorrectly spelled "Hospitial Morgue."