Continuity mistake: When Bart crashes at the social club, his skateboard changes position between shots. (00:05:30)
Continuity mistake: At the end, the barriers outside the tavern change position. (00:21:00)
Continuity mistake: During the Itchy and Scratchy cartoon, things change about the positions of the cats, the clothing, etc. (00:07:55)
Continuity mistake: When we first see the papers on top of Skinner, the jar of preserves is not visible anywhere. It is beside him in the next shot. (00:19:15)
Continuity mistake: Bart's bruised eye has healed by the time he reaches Skinner's office to lick envelopes. (00:02:40)
Continuity mistake: After Marge says she will marry Homer, at the beginning of the scene, the car is facing the power plant, and at the end, it is facing away from the plant. (00:07:45)
Continuity mistake: When the mobsters enter Skinner's office, the phone on his desk changes position between shots. Also, the name bar on his desk doesn't read anything on it. (00:13:50)
Continuity mistake: In the beginning, when Bart finds that the dog ate his homework, the poster on Bart's door has disappeared for one shot. (00:01:45)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: While Bart is in school, Sherri and Terri are making him comfortable. One of the twins vanishes for one shot, and their skin color keeps changing from white to yellow. (00:11:05 - 00:12:15)
Continuity mistake: In the episode which recalls how Homer and Marge got married, Homer writes a note to Marge on a piece of paper entitled 'From The Pen Of Patty' he SCRIBBLES out Patty's name and writes his own, but when Marge reads the note, 'Patty' only has a single straight line through it. The word "HOMER" also changes. (00:14:30)
Continuity mistake: Just after Bart has played the guitar in the street, he picks up two books. Before Bart picks them up they are green but they instantly turn blue when he does pick them up. Then when he gets on the bus the books have disappeared completely. (00:10:10)
Continuity mistake: At the beginning, when there is an overhead shot of the Simpsons' lawn, the broken lawn mower has disappeared. (00:01:20)
Revealing mistake: When Smithers makes Mr. Burns his Wine Spritzer, Burns makes Homer Employee of the Month. While Smithers is pouring the stuff in the bottle, his left hand turns black for three frames. (00:10:30)
Continuity mistake: When Homer and Barney are talking about the lottery, Barney says, "130 million." Then, they set their mugs on the table but when they all run off their mugs have disappeared. (00:01:50)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: In the parking lot, when Carl arrives, he is wearing a blue tuxedo. It changes to a lighter blue, and then back to its normal color when he gets in the car. (00:07:05)
Continuity mistake: When Burns first shows the team the nerve tonic, the "&" on the 'Brain & Nerve Tonic' label is facing backward, but as Burns pulls it away it faces forward. Then as he moves it around as he's talking, the "&" switches between facing forward and facing backward again. This happens all in the one shot.
Radio Bart - S3-E13
Continuity mistake: When Marge puts Maggie to bed, her pacifier changes from red to light brown between shots. (00:08:10)
Continuity mistake: As Martin reveals his Honor Rollor at the time trials, we can see Bart on the right side of the screen. He suddenly appears beside his car in the next shot. (00:13:00)
Lisa's Pony - S3-E8
Continuity mistake: Before Lisa licks the salt lick, there is another horse in the stable which disappears. (00:14:30)
Lisa's Pony - S3-E8
Continuity mistake: In the kitchen, there is a clock on the wall that changes time from 07:10 to 09:10. (00:12:10)
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