Ooooh, good and juicy thread! Sorry I don't know what is on the sound file you supplied, but I know about lots of other songs with odd/interesting/accidental background sounds.
One of the most famous would be "Love Rollercoaster" by Ohio Players (the original, NOT the Chili Peppers). Near the middle of the song, you can hear a woman's horrible scream in the background, and the urban legend popped up right away that it was the recorded death-scream of someone dying or being killed in the studio. The Ohio Players officially said, "Huh?" whenever asked about it, and sales of "Love Rollercoaster" went wild as morbid fans were desperate to hear the "death scream."
http://www.snopes.com/music/hidden/roller.htm
Near the end of "Strawberry Fields Forever," during the second fade-out, a voice appears to be saying "I buried Paul," which fueled a lot of the Paul Is Dead rumors. However, when the Anthology was released in 1995, it was easily proven that the voice was saying, "cranberry sauce," instead.
As mentioned in the Beatles Smackdown thread, the song "Girl" features the Beatles chanting the word "tit" as part of the background vocals (just to see if they could get away with it).
One sound that was NOT in a song that everybody claims to have heard was the infamous cricket accidentally captured on tape by Buddy Holly as he tried to record "That'll Be the Day" in his garage. That whole thing was completely fabricated (in addition to nearly everything else) for the Gary Busey movie.