Brother From Another Series - S8-E16
Continuity mistake: While Sideshow Bob is walking out of prison and towards the protesters, Carl's hair is red.
Brother From Another Series - S8-E16
Continuity mistake: Sideshow Bob's seat belt is on in one shot but gone in the next when he has been released from prison.
Continuity mistake: When Bart falls down the stairs, you see him fall down at least 50 stairs in the close up. There are never this many on the full shots of the staircase.
Continuity mistake: When Lisa arrives at Dr. Nick's, amongst the wheelbarrow line is a Professor Frink (and he's not even first in the cue). However, just a few minutes later, when Lisa ends up in the mud pit, we can see Frink amongst the crowd.
Homer vs. the 18th Amendment - S8-E18
Continuity mistake: When Homer and Bart are escaping from the cops after stealing kegs of beer from the dump, they drive through a cemetery and slam into a headstone, breaking the right headlight of the car. When they pull into the driveway back at Evergreen Terrace, the left headlight is the broken one.
Homer vs. the 18th Amendment - S8-E18
Continuity mistake: Carl and Lenny are seen at both Moe's and at the St. Patrick's Day parade, which are happening simultaneously.
Grade School Confidential - S8-E19
Continuity mistake: Edna Krabappel's name on the envelope is misspelled as "Enda" when Bart is opening and reading the letter, but is spelled correctly when viewed in close-up.
Continuity mistake: When Santa's Little Helper is taken away by the Repo Men, the van's back bumper is first seen to have no number plate. When the van drives off, there is a number plate.
Continuity mistake: When handing out the mail, Marge places a miniature jerry can of petrol on the table. It is gone in the next shot.
Continuity mistake: In the opening scene of the episode, envelopes are pushed through a mail-slot on The Front door. However, when Laddie arrives and Bart goes outside to meet him, The Front door's mail slot has disappeared.
Continuity mistake: The doormat at the Blind Man's house is initially coloured blue, but when Bart steps on the squeaky toy, look at the mat and you can see there is now a dark blue border around it.
Continuity mistake: When Bart sees Santa's Little Helper by the window at the Blind Man's house, the window frame is divided into sections but in the next shot it is plain.
Continuity mistake: When Bart goes to push the doorbell on the Blind Man's house, the doorbell is initially on the wall but in the next shot it is on the doorframe.
Continuity mistake: When Willy is speaking to Bart, you can see there is a plate in front of him when he tosses the bone away, but when we see Willy a couple of shots later, the plate has gone.
Continuity mistake: When Moe is talking to the Repo Depot Proprietor, the till on the desk changes position between shots.
Continuity mistake: When Bart arrives at the Repo Depot, he has nothing in his hand, but when he walks through the door, a photograph suddenly appears.
Continuity mistake: When Marge is speaking to Bart at the dinner table, there is a fork by Bart's plate that disappears in the next shot.
Continuity mistake: When Bart and Laddie are at the Springfield Town Hall, you can see there is nothing on the wall behind them, but in the next shot a plaque appears.
Continuity mistake: When Bart is talking to Milhouse in the park, there are two pine trees in the background. When we see the two a little later, the pine trees have gone.
Continuity mistake: When the man in the park throws a Frisbee for Laddie to fetch, the Frisbee can be seen falling to the ground, but when we see Laddie running, the Frisbee is back in the sky again.
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