I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: When the boys get to the top of the hill the light on The Front of the bike has shrunk dramatically since the first time we saw it at Bart's driveway. (00:00:55 - 00:02:15)
Continuity mistake: During the 'whose garter is this?' joke Patty and Selma appear behind the Simpsons. (00:20:10)
The Fat and the Furriest - S15-E5
Continuity mistake: When Homer realises that the bear was only agressive because of the electrical tag, they share a bear hug. The back of Homer's shirt is torn to tatters, and his back is bleeding. Immediately thereafter, the back of Homer's shirt is completely intact.
The President Wore Pearls - S15-E3
Continuity mistake: At the end of the episode Lisa gets on the school bus and in the back of the bus there is an emergency door with a small window in it. The following shot she starts singing out the back of the bus but the window has disappeared.
Treehouse of Horror XIV - S15-E1
Continuity mistake: After Homer tries to stab himself with the banana, he drops it. But when Nelson's clothes disappear, the banana has vanished.
Milhouse Doesn't Live Here Anymore - S15-E12
Continuity mistake: Milhouse is holding the Monopoly set in the Simpsons house. Then when his Dad comes in he isn't. Granted he could have put it down, but it isn't anywhere we can see, so he would have had to put it down behind the sofa which is somewhat unlikely.
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: When Snowball III drowns, the number of weeds and rocks in the fishtank changes between shots. (00:09:15)
'Tis the Fifteenth Season - S15-E7
Continuity mistake: When we first see the skating rink, it has Jasper, Disco Stu, Otto, Apu and Manjua, Sideshow Mel, a couple of children and two couples skating on it. In the next shot we see the Comic Store Guy split his trousers - he wasn't there before. (00:14:00)
Continuity mistake: In the scene where the Simpsons are sitting down to eat dinner, we see Bart pour tomato ketchup all over his potatoes. Then when the shot changes, we can see all the ketchup bottle and the corn has disappeared, and the ketchup has come off his plate. (00:04:50)
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: When Homer comes home in the Ambulance we can see there is a yellow logo on the back passenger door. In one shot it randomly disappears. (00:05:40)
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: In this episode it is shown that Snowball I is buried in their backyard, but in other episodes, notable the one where Sideshow Bob becomes mayor, it is established that she is buried in a pet cemetary.
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: The cats' graves change position. When Snowball II is buried, they're away from the the tree and near the fence. When Snowball III is buried, the graves are away from the fence and Snowball is among the roots of the tree. (00:04:10 - 00:09:25)
'Tis the Fifteenth Season - S15-E7
Continuity mistake: Homer looks out of his bedroom window at the skating rink he has built in his back garden. Homer and Marge's bedroom is usually at The Front of the house. (00:13:50)
Continuity mistake: When we first see the medicine cabinet in the Simpson's bathroom the hinges are on the left. When Homer pokes it with the wire it opens as if the hinges are on the other side. The last time we see it, when Lisa rescues Maggie, the door is missing altogether. (00:01:25)
Continuity mistake: After Lisa unlocks the bathroom door with the coat hanger, the puddle of "baby blood" (Pepto-Bismol) at her feet disappears in the next shot.
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: When Roofi is singing at the concert, the Roofi head on the curtain is facing the left. Later, it is facing the right.
Catch 'em If You Can - S15-E18
Continuity mistake: When Lisa says "It's called Wicca, and it's empowering" to Bart, her necklace is red instead of white.
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: In the bathroom, Lisa can't stand the Roofi CD being played so she pulls the plug out of the plug socket to stop the radio playing. In the next shot, the plug has disappeared from the radio. (00:02:15)
Diatribe of a Mad Housewife - S15-E10
Continuity mistake: When Homer goes to Ned to make sure Marge imagines nothing again, Homer puts his hand through the door, then he puts his hand through the mailbox, then Nelson puts his hand out to steal the doormat. Nelson puts his hand just over the mailbox, then in the next shot when it reveals Nelson is there, his hand is suddenly under the mailbox without enough time to move it.
My Big Fat Geek Wedding - S15-E17
Continuity mistake: When Milhouse is hit by the rock in class, the map behind him changes colors. This actually happens within the same shot between frames.
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