And Maggie Makes Three - S6-E13
Continuity mistake: When Homer remembers finding out that Marge was pregnant with Bart, he screams, tears out his hair and runs upstairs, past a picture of Lisa in the pink hat she wears to church. This mistake re-occurs seconds later when Homer remembers finding out Marge was pregnant with Lisa. Hard to have photos of Lisa on the wall before Bart and Lisa were even born...
Tree House of Horror V - S6-E6
Continuity mistake: In "Time and Punishment", when Homer returns to the basement after his first time travel, there is a scorch mark on the work bench where the toaster was placed when he turned it on. The angle changes to a shot from the stairs, and the scorch mark is gone. Later in the episode, the mark is back on the bench.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: Homer leaves the Simpson house to go to the farm house in the station wagon, and when he parks in front of the farm house he's driving his pink car.
And Maggie Makes Three - S6-E13
Continuity mistake: Bart comments on Homer's extreme reaction when he realised Marge was pregnant with Maggie. In the next flashbacks, when Homer reacts in the same way to hearing about Bart and Lisa, they are shown in the house at Evergreen Terrace both times. In Series 4, in the episode Lisa's First Word, they show that the Simpsons did not move to Evergreen Terrace until just before Lisa was born. Other episodes have also shown that Homer was with Marge at Doctor Hibbert's when she found out about her other pregnancies.
Springfield Connection - S6-E23
Continuity mistake: When Marge is lying on the sofa reading her book the red lamp behind her is first seen to be fully red.In a following close up shot it has an orange rim on the bottom of the shade.
Continuity mistake: Homer's two hairs over his head are dishevelled when the family arrive at Itchy and Scratchy land due to whatever has happened on the detour - however, it suddenly changes to being like he normally has it in the last frame that shows the family in the car, before the car park is shown.
Lisa's Rival - S6-E2
Continuity mistake: The position of Ralph's Star Wars action figures changes the two times they show his diorama.
Homer Badman - S6-E9
Continuity mistake: When Homer's badly-edited "Rock Bottom" interview is shown on TV, the hands on the clock behind him keep jumping around between all the different cuts. But when we saw him giving the actual interview earlier, the clock behind him stayed at 5 o'clock the whole time. The hands on the clock are also slightly different.
Two Dozen and One Greyhounds - S6-E20
Continuity mistake: There are twenty-six puppies eating from their bowls in the kitchen. As the title suggests, there's meant to be twenty-five.
Lisa's Rival - S6-E2
Continuity mistake: During the diorama show, they cut to a shot of Milhouse, and his glasses are broken and taped together. But when he's shown a second time, they are back to normal.
Homer Badman - S6-E9
Continuity mistake: Homers car gets blown over by a helicopter, and gets dented, and all the windows smash. But in the next overhead shot the car is parked on the side of the road, perfectly intact.
Springfield Connection - S6-E23
Continuity mistake: When the Simpsons are eating and the family are praising Marge, Homer's plate is first seen to have a small amount of yellow food and a bit of pink food (meat?).In a later shot when Homer steals and uses Marge's pepper spray he has a large pile of yellow food.
Continuity mistake: When Wolfcastle says that 'Jay Sherman insulted him, now he will die', for a few shots the shadows are on the floor before they magically disappear. Also, the shadow of the gun does not match the real gun.
Continuity mistake: When Homer is driving home in a bad mood (just before he gets stopped by Chief Wiggum), you can see that there is a pattern on the side of the car. In a next shot when Wiggum is walking alongside the car there is no pattern.
Continuity mistake: After Bart attempts to escape by using spray paint cans as rockets, his feet alternate between clean and spray-painted for a few shots.
Continuity mistake: When the Stonecutters are singing "We do", the position of several characters, particularly Number 51 and Chief Wiggum, change randomly as the camera angles change. Number 51 starts at the end of the table on the right side, with Chief Wiggum two seats to the left of him. In later shots, Number 51, then Wiggum are both switched to the same position, midway up the left side. Then, when the song ends, Wiggum has disappeared, and Number 51 remains in this new position.
Continuity mistake: In the scene where Lisa runs into the attic as she dives behind the chest she rattles a bird cage, later when Ned faints you can see that the bird cage has disappeared.
Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' when the machine picks up the Simpsons' house, to take it to the 'Re-Neducation Centre,' the garage is on the wrong side of the house. It is on the correct side in the following shots of Homer returning. (00:11:20)
Continuity mistake: When Bart and Lisa are looking at the globe, Bart points out Argentina and 'Ran McNally.' 1) Next time you see the globe, it is showing Africa and Asia 2) Asia is shown incorrectly and 3) The equator has disappeared.
Continuity mistake: When Homer and Marge are on the plane, they both have seat belts on. However, when Marge gets up to run up and down the plane, both seat belts have disappeared.
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