Continuity mistake: Mr. Burns gives Marge a present when she starts her new job. The present is light purple with a red ribbon around it. Seconds later though, the present turns to orange with a red ribbon around it. (00:11:45)
Continuity mistake: You may have to look carefully for this mistake. When Marge picks up the 'Das Butt' video, you can see the cover. In the next shot, you can see Marge holding it so you can't see the cover. But when she hands it over to Ruth, she twists the video round and you can see that nothing is visible. You may have to see it a couple of times. (00:04:50)
Sideshow Bob's Last Gleaming - S7-E9
Character mistake: Homer drinks 6 non-alcohol Duff at the air show, but is charged for 8.
Sweet Seymour Skinner's Baadasssss Song - S5-E19
Continuity mistake: In the air duct, the dog comes up behind Willie in a straight line and licks his feet, we saw what the duct looked like when Willie turned around. However, when the children start throwing stuff at the duct, from the outside there is a sharp bend right behind where Willie and the dog are that wasn't there in the internal shots.
Milhouse Doesn't Live Here Anymore - S15-E12
Continuity mistake: Milhouse is holding the Monopoly set in the Simpsons house. Then when his Dad comes in he isn't. Granted he could have put it down, but it isn't anywhere we can see, so he would have had to put it down behind the sofa which is somewhat unlikely.
Continuity mistake: When the bottle of bourbon is found and taken out of Marge's pocket, the bottle is grey. But when Sanjay throws it to Apu, and Apu catches it, the bottle has now changed to a brown colour. (00:08:30)
Continuity mistake: Homer opens the door on Bart just before he shows the kids his BBQ invites but there is never a door there in the Simpsons' home, only a doorway.
Continuity mistake: When Marge puts more lamb chops on Lisa's plate they are now grey in colour. Also the ones already on her plate have turned to grey.
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: When Snowball III drowns, the number of weeds and rocks in the fishtank changes between shots. (00:09:15)
'Tis the Fifteenth Season - S15-E7
Continuity mistake: When we first see the skating rink, it has Jasper, Disco Stu, Otto, Apu and Manjua, Sideshow Mel, a couple of children and two couples skating on it. In the next shot we see the Comic Store Guy split his trousers - he wasn't there before. (00:14:00)
Springfield Connection - S6-E23
Continuity mistake: When Marge dives under the garage door she leaves a blue estate car. The Simpsons have an orange estate car and a purple saloon, car not a blue estate.
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: There are several errors in the plant's parking lot: 1, in the overhead shot of the plant, we see Homer drive in, and there are parking barriers on the road. These disappear in the next shot. 2, As he drives in, there are at least eleven parking spaces on the right side of him. Carl takes up one spot, and in the next shot there are about 3 parking spaces left. 3, When he parks, we see several cars behind him, but in the shot before that, no cars are visible, not even parking spaces, and 4, when both Homer and Carl drive in, we see orange lines on the road, which weren't visible in any other part of the scene. (00:07:00)
Continuity mistake: When Barney enters the tavern, we see a guy working with Moe. His hands change position between shots. (00:16:15)
Other mistake: When we first see Nelson's Roadkill 2000, Nelson is moving backwards, though we see his legs as moving forward. (00:13:25)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Homer gets turned into a jack-in-the-box, we don't hear the chair he was just holding crash onto the floor. Bart doesn't make it vanish, as we see it on the floor when Homer is turned into a jack-in-the-box. (00:13:20)
Continuity mistake: There are many mistakes when Homer is checking for donut flavors, i.e. the positions of the donuts, the topping, etc. (00:03:50)
Continuity mistake: When Marge throws the Burly paper in the water, they start growing and sucking up the water. But the things inside that rolls don't grow.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Homer sees Marge and Moe near the end, the coffee table changes size between shots. It's large when Moe sits on the couch.It's smaller when there's a shot of Homer and long again when the high shot shows Homer walking out (when his rags are stuck on it)
Mr. Lisa Goes to Washington - S3-E2
Factual error: When the piano keys are shown when it is played at the end of the episode, it is shown having one black key each time. Real pianos start off with three black keys, then two, then three and so on.
Homer's Triple Bypass - S4-E11
Continuity mistake: When Homer is having his operation, and Dr. Nick says, "I know I'm supposed to cut something, but what and where?" his moustache disappears three times. (00:19:50)
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