Lisa on Ice - S6-E8
Corrected entry: When Homer is signing Bart's academic alerts, you can see that the writing on them is complete gibberish.
Corrected entry: When Aunt Gladys Bouvier dies, she leaves her pet iguana to her sister, Jacqueline Bouvier (Marge's Mom.) If she never married as she claims, Jacqueline's maiden name would have been Bouvier, not her married name. This would also mean that Patty, Selma and Marge would not be Bouviers either.
Correction: It is customary for the wife to take the husband's last name, not mandatory. You can even switch back after a divorce or a death.
RlvlkCorrected entry: In the opening part, you see Lisa playing a trumpet, there is a boy to the top right of her, when it cuts to the conductor you can see the same boy in the background.
Corrected entry: In the opening sequence which turns into a large circus (as seen in "Bart After Dark" and "Cape Feare") the elephants in the background don't have any tusks.
OL1V3R666Correction: Most times the tusks are removed for circus performing elephants. They don't want to have a trainer impaled on the tusks. Also, Female Asian elephants usually lack visible tusks, as do males in some populations.
Corrected entry: Neither Barney nor Homer underwent any sort of physical or medical examination at all. Homer has a heart condition, he has had bypass surgery, and yet he is still allowed to take part in the mission. Also, both of them are surely too overweight to be allowed to participate.
Correction: The whole mission wasn't well thought out to begin. At the end of the day they were looking for a "Blue collared slob" to attract fans, and in that case Barney and Homer were perfect. The fact they were overweight and in average health was not NASA's main concern. Also they do undergo examinations but we probably don't see all of them. One scene we see them doing a lung capacity test.
Lummie
Corrected entry: At the start of the episode, the Simpsons celebrate finally paying off their first mortgage. But earlier in "The Computer Wore Menace Shoes", the credit card machine said that Homer was on his fifth mortgage.
Correction: True. They still have four more mortgages to pay.
XoferCorrected entry: Moe says there hasn't been a woman in the bar since 1979, implying that the bar has been around for at least a couple decades. But in a later episode, a flashback shows that Moe's grand opening was nine months before Bart was born. And we all know Bart is 10.
Dude, Where's My Ranch? - S14-E18
Corrected entry: When Lisa tells Marge about Luke for the first time, Marge says 'I didn't marry the first boy I - Well I did. But you shouldn't." Wrong. Before she had a crush on Homer, she loved Artie Ziff from high school. She didn't marry him, however. Everybody blatantly knows that Marge married Homer, her second crush.
OL1V3R666Correction: Homer was her first love. She never admitted to loving or having a crush on Artie Ziff. Marge went to the ball with Artie in spite of Homer and what he did to her but she never loved Artie and never admitted to loving him. Also in the statement she makes she never admits to anything. Its presumptious she was going to say the first boy she had a crush on. It could have been the first boy she had a real relationship with.
Lummie Corrected entry: When Flanders is singing in the church, the tune is one flat note and his mouth is continually opening and closing
Correction: Flanders doesn't completely close his mouth when singing, and he is probably just breathing at the same time.
OL1V3R666The Seven-Beer Snitch - S16-E14
Corrected entry: For "The Seven-Beer Snitch": During the faked breakout, every prison guard is outside, so who pulls the switch to open the cell doors? All the prisoners were in their cells.
Correction: We see a prisoner pull the lever from inside his cell.
Last Exit to Springfield - S4-E17
Corrected entry: When we see a flashback of Mr Burns' ancestor in 1909, he looks at atoms from someone's pocket. Actually, atoms are smaller than microscopic so it would have been impossible for him to see the atoms through a magnifying glass.
OL1V3R666Correction: That is what is technically known as the joke... Or, to be more specific, it is obvious that the elder Burns have no idea what he is talking about, or for that matter what nuclear science is about (seeing how he has men trying to split atoms with sledgehammers). Then, when he discovers crumbs or regular pocket lint in the employee's pocket, he believes that this is the miraculous "atoms" he has heard about and assumes that this working-class lowlife has been stealing from him. Ridiculous, as everybody who knows the first things about atomic science knows, but that's what is funny in the scene.
TwotallHomer's Barbershop Quartet - S5-E1
Corrected entry: When the people are protesting at Moe's Bar, you can see several arms that aren't attached to bodies.
Correction: We can't see the bodies that the arms belong to becuase of the people standing in front of them, so we don't know whether there are bodies there or not.
OL1V3R666Corrected entry: When Marge asks Homer to open the door for her sisters, he says "Patty. THELMA." (The English captioning has that mistake as well, but is correct in the Spanish captioning) (00:03:30)
Correction: He actually says Selma, and the DVD English subtitles (in Region 2 at least) also say this. Listen closely.
Three Men and a Comic Book - S2-E21
Corrected entry: When Bart is pulling the weeds out by hand, the secateurs that he couldn't use have totally dissapeared from the floor.
Correction: Although very hard to see, if you look closely to the bottom-right of the screen you can see the secatars when Bart first cries out in pain.
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Corrected entry: In "Clown Without Pity", where the Krusty doll acts as Homer's servant, Homer says at one point "Yeah, dogs like to bury old junk", in which the Krusty doll says "Yeah, you stupid idiot.." The 'you stupid idiot' part is said with his mouth closed. (00:07:15)
Corrected entry: When Bart makes a phone call to the Australian boy, it is daytime in both Springfield and Australia. However when the Australian boy's father phones Bart, it is again daytime in Australia but night-time in Springfield. But due to the Earth's rotation, surely it would have to be night-time in Australia or possibly very early in the morning. It seems to remain daytime there.
OL1V3R666Correction: The phone calls are made at different times from each other so judging the time zone differences is tricky. However it is possible for the scenes to have daylight in both regions and daylight/night as in the show. If you use New York as reference point, a phone call at 4:30 pm, the call would be receieved at 6:30 am in Australia when it is plenty of time to have sunlight. When the Australian father calls it would be the afternoon and early morning in Springfield. If a call at 4:30 pm from Austrlia, it would be 2:30 am in New York.
Lummie Marge vs. the Monorail - S4-E12
Corrected entry: When Lurleen is talking to Kent Brockman, her voice is completely different than how we heard it in "Colonel Homer".
OL1V3R666Correction: This is intentional. The hoarse, scratchy voice (along with "I spent last night in a ditch") is supposed to denote how rough her life's been since "Colonel Homer".
XoferItchy and Scratchy: The Movie - S4-E6
Corrected entry: How exactly did the chair from Miss Hoover's classroom get stuck to Homer's backside? There was nothing sticky on the chair when we first saw it.
OL1V3R666Correction: His rear end was so fat it got wedged in the seat.
XoferCorrected entry: When Mr Burns' hounds chase Ned Flanders, they jump across the screen and simultaneously growl. However their mouths don't move when growling.
OL1V3R666Correction: Having owned various dogs for 30 years, I can tell you that a dog's mouth does not have to move for it to be able to growl. The growl comes from deep in their throat.
GuyThe Old Man and the C Student - S10-E20
Corrected entry: In this episode, Hans Moleman is in a retirement home. But in "Duffless", he reveals that he is actually 37 years old, and therefore is too young to be in a retirement home.
OL1V3R666Correction: Being that there is no age restriction in being in a retirement home there was nothing stopping Hans from moving into the home. The reason could be that Hans is weak, slow and has poor eye sight. With all these ailments he perhaps decided that he needed specialist care that a retirement home could provide.
Lummie 
Correction: Homer only has to sign the forms, not print anything out. It could be how he signs them.