Continuity mistake: When Homer is fishing, the colours of the things on his hat switch places between shots.
Continuity mistake: When Frink collapses at the table, his sleeves are green. When it cuts to a wide shot, they are yellow.
Continuity mistake: When Bart and Lisa are in the compound, just before Bart gets brainwashed, the bags that were behind Lisa disappear. Homer and Marge were on the other side of the room, so they couldn't have picked them up.
Bart Carny - S9-E12
Factual error: Sharks cannot just reverse backwards like that one did under the glass bottom boat. The only way sharks can go backwards is either swimming around in a circle or allowing the current to carry them.
Lisa's Sax - S9-E3
Plot hole: In this episode, Homer repeatedly says that they have no air-con or thermostat, but we saw that they had a thermostat in the first clip show episode. What happened to it?
Bart Carny - S9-E12
Continuity mistake: When Homer is talking through the door to Cooder about getting the house back, the shot is through the fisheye lens on the door and you can see Marge, Bart and Lisa smiling. The very next shot, they suddenly have a frown in no available time.
Other mistake: When Homer is muttering whilst walking up and down the home landing at night after being told he has to wait 5 days to receive his gun/license, Lisa being awoken by his muttering complains that it is 3am but her bedside clock shows 9.50/21.50. (00:06:55)
Homer's Triple Bypass - S4-E11
Factual error: I get it, it's a comedy. But after open heart surgery, you are sedated for 1-2 days and on a ventilator. So, Homer even being awake after open heart surgery is completely false. Also, as someone who has had open heart surgery, you can barely move your chest because your sternum is fractured.
The Last Of The Red Hat Mamas - S17-E7
Factual error: Milhouse says he speaks fluent Italian, but his Italian is full of basic grammatical errors. He says that "insegnante" means "masculine teacher" when the same word is used for a male or female teacher. There are errors in Lisa's Italian course too ("barca piccola" instead of "piccola barca"). Despite Lisa's understandable mistakes, as she is a learner, Milhouse never corrects her (there is no such word as "idioto"). Even Milhouse's grandmother, who is Italian, makes many grammatical mistakes.
Other mistake: At the finish line, the crowd are missing all their appearance features such as faces, hair etc. (00:13:50)
The Day the Violence Died - S7-E18
Other mistake: At the end of the episode Lisa and Bart watch Itchy and Scratchy in the TV room, which is beside the kitchen at the back of their house. The TV room has a window that faces the backyard, with the record player on a shelf in front of that window. The problem is when Bart looks out the back window and sees Lester skateboarding past the house, the view outside is actually the street in front of the Simpson house, not their backyard as it should be.
Other mistake: At the concert when Bart throws the Frisbee into the dude sat next to him, the crowd in the background are all missing their eyes. (00:03:50)
Continuity mistake: When Marge spots Krusty, from the regular view, Krusty's hand is down on the table. But from the view from the camcorder, his hand is on top of the cake. (00:14:00)
Other mistake: In the scene set in the future after Lisa, as the US President, held a conference with some journalists, just before the scene changes they show a black journalist with eyes not drawn among the crowd.
Continuity mistake: When we see Marge leave Bart with Patty and Selma, they are stood with a gap between them. Camera changes to focus on the sisters, and they are now next to each other. (00:06:30)
Other mistake: When Homer pretends to read the newspaper, the back page is very noticeably blank and missing any print. (00:08:00)
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."
Brother From Another Series - S8-E16
Continuity mistake: In the shot where Homer yells, "Marge, I'm going to look for the kids," their door is shut. After Homer sees the wave and runs back inside, their door is open all of a sudden.
22 Short Films About Springfield - S7-E21
Other mistake: When Chalmers and Skinner are having lunch with hamburgers, Chalmers bites it. When he opens it, the bread's slice is bitten but the meat is not.
Answer: I'm not sure if this is the one you're thinking of, but an episode of "Ray Bradbury Theatre," called "A Sound of Thunder," dealt with a similar matter: a group of hunters travel back in time to hunt dinosaurs, only to find things have changed when they get back because someone stepped on a butterfly.
Xofer