Continuity mistake: At the BBQ, Homer lights the grill on fire with a match. When Lisa walks out with the bowl of gazpacho, the fire instantly disappears. (00:13:05)
Continuity mistake: When Bart visits the kid's train ride, the first shot of it shows that it starts with a big curve before the tunnel. When he goes on it the track is straight before the tunnel.
Continuity mistake: When we first see Homer feeding the can to the goat the background shows a wooden coop. In the next shot, a purple tree stump appears there too.
Continuity mistake: When Lisa is first seen petting the baby lamb, she is next to the fence with hay beside her. In the next shot, she's far away from the fence and there's no hay anywhere.
Continuity mistake: After Homer prepares the BBQ he holds out the steak and holds it back in as Lisa speaks. When the shot changes he's holding it out again, and the pile of meat behind him is smaller and has moved slightly under the window.
Continuity mistake: During dinner Marge has no glass to her right. When she says 'Why thank you Homie' a glass has appeared next to her.
Continuity mistake: Throughout the dinner scene, whenever Homer wants the syrup, it disappears and re-appears next to Lisa.
Continuity mistake: Lisa places her Gaspacho on the house end of the table but in a following shot it's at the other end when the dog is drinking it.
Continuity mistake: When Skinner is addressing the class before the meat video we first see him with black trays on the desk to the far right. In the next shot they're much closer to him.
Continuity mistake: When Lisa knocks Bart's chop out his mouth she knocks it out front, however, the chop ends up going to the far right and into Homer's mouth.
Continuity mistake: When Homer is talking to Ned about having his own BBQ Ned is facing the fence but in the next shot he is facing alongside it with his head turned to Homer.
Continuity mistake: On Lisa's plate at dinner she has no mashed potato. During the lamb vision, her pork chops are now smaller and there's now mashed potato on her plate.
Continuity mistake: When Lisa knocks the lamb chop out of Bart's mouth to Homer's it changes colour during the journey.
Continuity mistake: In the Meat video Jimmy's steak is first seen to be a little thin. In the closeup it's very thick, then thin again in the next shot.
Continuity mistake: When Maggie's dummy is spinning after the goat has taken her, the ground is clear. In the next close up shot there are tufts of grass and clumps of dirt there.
Continuity mistake: When Lisa starts to drive away with Homer's pig, Marge is screaming 'No.' On Lisa's close up we can see Marge briefly to the left of the screen and her mouth isn't shouting.
Continuity mistake: When Lisa is with Apu, Paul and Linda the wall behind her is purple.On a close up of her when she's listening to Apu it's blue.In the next shot it's purple again.
Continuity mistake: During the lamb vision at dinner Lisa is holding her knife and fork. In the very next shot they're on the table.
Continuity mistake: Wiggum asks Homer for another burger and Homer throws it to him. When he catches it Otto has disappeared from sitting next to Eddie.
Continuity mistake: When Homer opens the door on Bart the door handle is purple with a grey backing. Later when Homer is saying 'If I went to a BBQ and there's no meat...' there is only the purple knob.
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