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)
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)
Continuity mistake: When Lisa comes down the stairs prior to watching "When Buildings Collapse", the TV screen is near enough in the corner of the living room and can be seen from the stairs. When Lisa enters the living room, the TV has moved further into the room. Subsequent shots of the TV move it so far into the room that it would not have been possible to see it from the stairs at all in the first place.
Audio problem: In the U2 scene during the end credits, when The Edge says "oh, here we go" his mouth is not in sync with his voice.
The Trouble With Trillions - S9-E20
Continuity mistake: The To Do Pile doesn't appear until Marge mentions it.
Continuity mistake: When the "Angel" tells everyone to prepare for the end, Carl is seen with yellow skin.
Continuity mistake: While everyone in Springfield is waiting for the apocalypse, Dr. Hibbert's wife Bernice is seen with yellow skin while she's holding on to him.
Continuity mistake: When Dr. Gould says the DNA test was inconclusive, Apu is seen in the background with yellow skin.
The City of New York vs. Homer Simpson - S9-E1
Revealing mistake: Homer drives his car through the man at the picnic.
Continuity mistake: When Kent Brockman gives his after thought on Lisa's speech, his hair and clothes have changed colors.
Continuity mistake: At one point when Homer is giving his speech in front of the Jebediah Springfield statue, Carl's skin is yellow. In all other shots he is back to his normal color.
Continuity mistake: At one point, while everyone is clapping for Homer during the debate in The Town hall, Apu is seen with yellow skin, and Chief Wiggum is seen with black hair among the townspeople. In all other shots, they're back to their normal skin and hair color.
Continuity mistake: Bart, Lisa and Milhouse run away from the others and are stopped by a cliff. Milhouse then grabs onto a vine which was never there in previous shots. (00:19:00)
Continuity mistake: At the trial, Milhouse moves over to Lisa and Bart is in the middle of them. In the next shot, Bart has disappeared. (00:15:25)
Continuity mistake: Everyone discovers Milhouse ate the food so they walk up to him. The shot cuts and they are further away than they were in the previous shot. (00:13:50)
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