Lisa's Pony - S3-E8
Continuity mistake: When applying for the loan, a bell appears on the counter in front of Homer. (00:10:00)
Other mistake: Right before Homer and Bart head to the concert, Homer has the high-pitched ringing in his ears while Marge is talking. Then just as Homer says, "I hear you. C'mon, boy," note Selma's and Patty's skin over their scoop necklines are not colored in properly, it's the same color as their dresses. (00:01:45)
Continuity mistake: While Otto plays the guitar at 3:00 AM, the tuning keys on the guitar head are first facing down, then the guitar head flips and the tuning keys are facing up, between shots. (00:15:45)
Brother Can You Spare Two Dimes? - S3-E24
Continuity mistake: When Homer says he doesn't know what the one light switch does he flips it and it shows a merry Christmas message on his roof. However, in subsequent shots, there are no lights attached to the roof. (00:12:50)
Brother Can You Spare Two Dimes? - S3-E24
Continuity mistake: When Marge says that the money was a blessing, and they can't waste it, the arm covers on the chair change size between shots. (00:10:40)
Brother Can You Spare Two Dimes? - S3-E24
Revealing mistake: When Herb reads the article about Homer winning the $2,000 the writing on the newspaper (except the headline) is just gibberish. (00:09:20)
Brother Can You Spare Two Dimes? - S3-E24
Continuity mistake: At the start of the awards ceremony, Mr Burns and his podium emerge from nowhere on the stage. (00:07:20)
Brother Can You Spare Two Dimes? - S3-E24
Continuity mistake: When Herb mentions about "new coke" the homeless man who makes a comment looks like no-one in the group Herb is talking to. (00:03:50)
Bart's Friend Falls in Love - S3-E23
Continuity mistake: When Bart admits to Milhouse that he narked on him and Samantha he is facing the bed. When the camera changes, he has turned 90° and is no longer looking at the bed. (00:19:00)
Bart's Friend Falls in Love - S3-E23
Continuity mistake: When Millhouse asks Samantha if he can walk her home, his glasses are well above his ear. As the camera changes his glasses are now lower. (00:07:20)
Continuity mistake: Bart's guitar disappears when Otto starts to race to school. (00:11:15)
Continuity mistake: When the band is talking to the audience about being the 6th member of Spinal Tap, the water on the stage simply vanishes between shots. (00:06:55)
Continuity mistake: When we see Homer in the car for the 1st time since the band hit the stage, he has his hand up in the exterior shot but in his bag of crisps from the interior shot. (00:05:20)
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 tells Otto to get a job, the books on the bookcase by Otto change/move between shots. (00:16:50)
Continuity mistake: When Otto crashes the bus, there is no sticker on the bumper. When the bumper flies off, a sticker has appeared. (00:11:30)
Continuity mistake: Selma says she wants a separation while leaning forward with her arms behind her. Camera changes and she is stood with her arms closed. (00:18:40)
Continuity mistake: When Bart realises Selma has 1 hour to live, the remote Patty is holding disappears as the camera zooms into Bart. (00:17:50)
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)
Continuity mistake: When Bob is litter picking, the amount of litter by his feet changes drastically between shots. (00:03:20)
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