Continuity mistake: When the Simpsons are on the raft going down the river in Africa they come to a fork and have a choice of going to the left, towards a sunny and nicer area or to the right where it is rainy and gloomy. As Homer tries to steer the raft to the left as he pulls his left arm out of the water and it is covered in leeches but in the next shot of him when we see the arm again the leeches are gone. No way to remove leeches that fast.
Continuity mistake: Patty and Skinner go to see 'Space Mutants IV: The Land Down Under'. In a season one episode, 'The Telltale Head', a sign on the Springfield Aztec movie theater reads 'Space Mutants IV: The Trilogy Continues'.
Home Away From Homer - S16-E20
Continuity mistake: We see Coach cutting down trees in Flanders' former driveway. However there had never been any trees in Flanders' driveway.

Lisa's Pony - S3-E8
Continuity mistake: The number of knives that Sherri is holding changes between long and close shots at the talent show. (00:04:50)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Homer is at the vending machine, in certain shots he is wearing a tie and in others he isn't. (00:02:20)
Continuity mistake: When Red has finished the steak, he lies back and is the same position for Homer's small speech. However, as soon as Homer starts to say 'Wait, you're not breathing,' Red blinks when he is meant to be dead.
Continuity mistake: When Homer and Marge are in bed Marge moves up and we can see she isn't wearing anything, but in the close up you can see that she is wearing her pyjamas - note the thing around her neck, then it's back to nothing.
Continuity mistake: After the slinky leaves Moe's hands, and goes out of Maggie's room, we see that Maggie's toy phone is right next to the door way, then when the camera goes towards Moe, and Maggie, then we see the toy phone next to Moe and Maggie.
The Mook, the Chef, the Wife, and Her Homer - S18-E1
Continuity mistake: When Bart and Fat Tony's accomplices are going to meet Krusty, Krusty's nose can briefly be seen as white when it should be red.
Cape Feare - S5-E2
Continuity mistake: When Bob has finished singing the score of the H.M.S. Pinafore, an English flag comes down. But when he draws his sword to kill Bart, the flag is gone. Where could it have gone?
Continuity mistake: When Barney becomes his old self again at the training center, he gets on a jetpack while holding a bottle. In the next shot while he is in the air, the bottle is gone.
Continuity mistake: When the school bus drops off Bart and Milhouse at the Simpson house, Bart puts his backpack on frontwards and starts krumping. When he walks through The Front door, he is still wearing his backpack on his front. It then cuts to inside the house, and we still see him coming through the door, but the backpack is gone.
Continuity mistake: When the men from Festival Cruise Lines arrive at the Simpson house, they park in the left-hand lane (closest to the house) with the car facing oncoming traffic, seen both when they first pull up and, more, in the background while informing Milhouse about his parents. But in the overhead shot of the house, the car is parked the other way around, following the direction of traffic.
Treehouse of Horror XXI - S22-E4
Continuity mistake: In the second segment, after Roger has told them about what happened to him, a radio appears out of thin air.
Treehouse of Horror XXI - S22-E4
Continuity mistake: In the second segment, as Roger is telling them about what happened to him, as he finishes the story of Marge and Homer saving him, in his recount Marge is wearing a shirt and bikini bottoms (the shirt is covering the bikini bra). But when they saved her, she was just wearing a bikini.

The Nightmare After Krustmas - S28-E10
Continuity mistake: When Krusty is in the hospital, the style of his bed rail changes. (00:04:20 - 00:05:35)

The Nightmare After Krustmas - S28-E10
Continuity mistake: When Homer moves Maggie's crib closer to the gnome, the wall outlet under the light switch has nothing plugged in, but in the next shot as Homer exits the bedroom, a nightlight is suddenly plugged in. (00:10:20)

The Nightmare After Krustmas - S28-E10
Continuity mistake: While Krusty is in the hospital talking to Sophie, he pops the IV line from his arm so the tubing hangs down from the fluid bag. But when Krusty tells Sophie that he knows she's reaching out, suddenly Krusty's IV line is properly inserted in the cannula again, only to change back to the tubing hanging down. Also, the white pillow propping up Krusty's foot vanishes and reappears during these shots. (00:05:15)

The Nightmare After Krustmas - S28-E10
Continuity mistake: When Bart opens the door for Krusty and Sophie, Bart is standing on a floor mat, but in the next exterior shot, that indoor floor mat has vanished. Other changes include the cane's handle within Krusty's grip facing the opposite way, as well as Krusty's and Sophie's positions at the outdoor purple mat. (00:06:50)