Continuity mistake: In the scene where Homer decides he wants to stay with Lurlene, she locks the door about 3 times before going to kiss Homer, but when Homer leaves, he just opens the door, he doesn't unlock anything.
Continuity mistake: After Lurleen sings 'No-One Understands You', she puts on her apron and picks up a tray. On the tray, there are three bottles of beer. But in the next shot, Homer goes over to Lurleen, and there is only a cup. (00:07:15)
Continuity mistake: When Homer and Marge are entering the cinema, Marge is taking Maggie with her. But when watching the film, Maggie is nowhere to be seen.
Continuity mistake: When the family are driving home from the cinema, Bart draws an angry face on the back of Homer's head. It is never there at any other point in that night.
Continuity mistake: When Lurleen is in the studio with the Simpson family, Homer has his arms crossed. When Bart asks to do a solo his hands are now in his pockets. (00:14:50)
Continuity mistake: As people throw stuff at the redneck bar, the guy who introduces Lurleen is leaning to his left then instantly to his right between instant cuts. (00:06:10)
Continuity mistake: When Marge and Homer are arguing over his boyhood dream, the time on clock jumps forward between shots. (00:13:20)
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