It might not have been a final, but Jim Joyce's infamous safe call on what would have been the 27th and final out, cost Armando Galarraga what should have been only the 21st perfect game in Major League Baseball history. Given that there is some 162 games played by each team in a season and 2,430 in total (that's just the regular season too), the rarity of a perfect game is huge, so it was a pretty significant stuff-up. Even more so, when replays clearly show the runner was out on 1st by a good stride.
http://en.wikipedia.org/wiki/Armando_Galarraga's_near-perfect_game
http://en.wikipedia.org/wiki/Armando_Galarraga's_near-perfect_game