Much Apu About Nothing - S7-E23
Continuity mistake: When the mob come to Quimby's office for the first time, the items on his desk change colour and position.
Much Apu About Nothing - S7-E23
Plot hole: At the end Apu finds out he's been chosen for jury duty for the first time. However, in 'The Boy Who Knew Too Much' he was on the jury.
Much Apu About Nothing - S7-E23
Continuity mistake: Willy jumps in and shakes his fists at the children and Skinner who are in a circle around him. Uta has now disappeared from the circle and cannot be seen anywhere when he was there just seconds before.
Much Apu About Nothing - S7-E23
Continuity mistake: When Kearney buys the beer, the shot of the ice cream sandwiches melting in his arm pits shows that the 'Duff' writing on the crate of beer is thinner than previously seen.
Much Apu About Nothing - S7-E23
Continuity mistake: When they are locating 'Springfield' on the map the coffee jug on the table is about 1/4 full.In the last shot of Apu the coffee has risen to about 3/4 full.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob leave Quimby's office, he had loads of things on his desk. When he pulls the picnic basket up, the desk is empty.
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer comes home with Apu, Lisa closes the book she's reading and slides it to the side on the sofa. When she stands in the next shot,the book has gone.
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer,Barney and Moe are in Moe's making signs Moe says 'But they ain't bothered...' and leans on the pool table with his elbow.In the next shot he is leaning on it with his hand.
Much Apu About Nothing - S7-E23
Continuity mistake: When Barney is tranquilised, he falls with his mouth closed. In the following shots, it's open, closed, then open again.
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer swings on the electric cable when attempting to get to his car, the cable has just appeared from nowhere because, the previous 'birds eye view' shot showed no cable.
Much Apu About Nothing - S7-E23
Continuity mistake: When Ned is struggling to get in the house at the beginning the door knob is light brown, then dark brown in another shot.
Much Apu About Nothing - S7-E23
Continuity mistake: When Apu introduces Professor Frink there are people either side of him but no Apu. In the very next shot Apu has appeared from no-where and is standing beside the Professor.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob come back to Quimby to complain about the 'Bear Tax' he opens the left door inwards.In a following shot both doors open outwards.
Much Apu About Nothing - S7-E23
Continuity mistake: When Apu awakes, he has a closed note pad, and the table looks small. In the next high-angle shot, Apu's book is open and face down, with paper on top of it and a pen beside it. The table is also bigger, with Bart sitting there with his breakfast things too.
Much Apu About Nothing - S7-E23
Continuity mistake: When Nelson pulls back Uta, he drops a book. In the next shot, the book has gone.
Much Apu About Nothing - S7-E23
Continuity mistake: When Apu and Lisa go to the 'Immigration Centre', they pass Dr Hibbert on the right, and he has yellow skin. In the next shot, his skin returns to its proper brown colour.
Much Apu About Nothing - S7-E23
Continuity mistake: When Bart pulls out Apu's punch cards, there are many sitting on top of the box. When Apu picks the box up and places it in the bin, there are only a few cards sitting on top.
Much Apu About Nothing - S7-E23
Continuity mistake: Homer comes to the Kwik-E-Mart with the new 'American Apu' and sees him reading a magazine. When Apu walks over to Homer, his magazine disappears.
Much Apu About Nothing - S7-E23
Continuity mistake: In the early scene where the Simpsons are gathered around the table to eat, you can see that they are eating slices of pie. However, on some of the long shots, the food on their plates changes and looks more like mashed potato and vegetables. Also, in the same scene, in one shot of Lisa, you can see Bart's hand over her plate, but when the angle changes, it is behind her plate.
Much Apu About Nothing - S7-E23
Continuity mistake: In the final high-up shot of the Simpson's garden with everyone chanting 'No on 24'; Lisa has disappeared from next to Apu, and Ned Flanders' glasses have vanished.
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