Continuity mistake: Homer goes to ring the phone number '1-909-WIN-BIGG' but we see he only presses four dials, and that's all we hear too.
Revealing mistake: When the announcer says that the Falcons win, he says "Who would've thunk it" Homer says "My daughter, that's who". When he is saying this, Lisa's arm disappears twice. (00:10:05)
Revealing mistake: When Homer leaves the bar after the Superbowl, as he goes through the door, the background is missing. It's just a brown background. (00:20:00)
Continuity mistake: Just as Barney asks Homer if he wants to go bowling next Sunday, Moe's boot disappears from the bar and the money appears in Homer's hands off the bar. (00:12:20)
Continuity mistake: When Homer gets off the phone to Moe, all the snacks he had have simply gone beyond a few remaining bits. (00:02:00)
Continuity mistake: At the bar when Homer is watching the superbowl, his hands keep changing position between the shots. (00:19:00)
Continuity mistake: Homer picks up Lisa who puts her Malibu Stacey down on the bed. When Homer puts her down, the doll and house have disappeared. (00:16:30)
Continuity mistake: When Homer goes to apologise to Lisa, he walks into her room and leaves the door open. As he steps inside however the door is now closed. (00:15:50)
Continuity mistake: When Lisa is lying on the floor, she has 3 pieces of paper/notepads with her. Once she starts to ring Moe though, there are only 2 pieces of paper on the floor. (00:12:05)
Continuity mistake: When Homer is yelling at the TV about being wrong 48% of the time, the colours of his beer can are reversed. (00:03:40)
Continuity mistake: At the start, the design on Homer's beer can change. Note the white stripe. (00:00:55)
Continuity mistake: When Homer is eating the snacks at the start, he drips some dip on the sofa that vanishes when Marge appears. (00:00:50)
Continuity mistake: At the start, the remote on the sofa next to Homer simply vanishes and returns when Marge walks in. (00:00:40)
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