Continuity mistake: Barney is simultaneously seen at the wrestling stadium watching the fight, and at Moe's.
Continuity mistake: While Edna is holding the "Goddess Bar", her shirt sleeves are pink like her pyjamas, but in the next shot, she is wearing her usual green outfit.
Continuity mistake: When Homer says "I will never know the score!" the bag of chips turns from green to blue.
Revealing mistake: When Alberto says "If you had completed your seduction of me, I never would have met Sylvia," his shirt collar briefly turns into the same color as his blazer.
Continuity mistake: In Bart's room, while Lisa is carrying the Krusty phone, the back of the phone Krusty's neck changes from white to yellow multiple times in the same shot.
Sex, Pies and Idiot Scrapes - S20-E1
Continuity mistake: During the St. Patrick's Day parade, Bart is wearing a green shirt throughout the whole scene, but he's wearing his usual orange shirt when he says "Where's the IRA when you need them?"
The Seemingly Never-Ending Story - S17-E13
Continuity mistake: When Lisa pets the goat after it returns her necklace, her pink jacket is missing, in the next shot, she has the pink jacket on.
Homer's Paternity Coot - S17-E10
Continuity mistake: When Dr. Hibbert is about to reveal the results of the paternity test, Mason Fairbanks is wearing a blue blazer and black pants. But, when Dr. Hibbert points at him and says "This guy", he has a light blue sweater and blue pants.
Milhouse Of Sand And Fog - S17-E3
Continuity mistake: Homer's chicken pox disappear when he puts the food into the suitcase.
Continuity mistake: When Cameron is being booed, Lenny's five o'clock shadow is missing, it returns in the next shot.
Continuity mistake: After Lisa's final performance, Bernice Hibbert (sitting next to Dr. Hibbert) has light brown hair instead of black/dark brown.
Continuity mistake: After Lisa's last performance, Carl and Lenny are seen with grey hair.
Continuity mistake: After Lisa finishes singing her song during the audition, there are several coloring mistakes in the shot of the audience clapping. Agnes Skinner's face is ghost white, but her hands are yellow. Mayor Quimby's suit is lavender instead of violet/blue, and his hair is light brown instead of medium brown. Helen Lovejoy has blonde hair instead of grey, and is wearing a purple shirt instead of pink sweater over blue shirt, and Reverend Lovejoy has a green shirt instead of pink, and has brown hair instead of black.
Don't Fear The Roofer - S16-E16
Audio problem: When Marge says "You're drooling on my goodwill pile", her mouth doesn't match her voice.
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.
A Star is Born-Again - S14-E13
Audio problem: When Homer tells Ned "Flanders, I'm always interested in talking about free milk. And if there's cookies involved, so much the better", his mouth is not in sync with his voice.
Strong Arms of the Ma - S14-E9
Audio problem: When the woman who smashes the piano says "support the arts", her mouth is open, but it doesn't move.
Little Girl in the Big Ten - S13-E20
Other mistake: Sherri and Terri are seen participating in the second grade gymnastics (as referred by the gym teacher), even though they're in the fourth grade.
Half-Decent Proposal - S13-E10
Audio problem: The lady singing at the prom doesn't move her lips when she sings, her mouth just stays open.
Continuity mistake: When Duffman says "Duffman can never die, only the actors who play him", his red briefs are missing.
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