Reply #4: I have heard it

[NJmaverick]

Etymology

The term was first documented in the early "Mercury" days of the US space program. It came there from a Yale graduate named John Rawlings who helped design the astronauts' space suits. The phrase is actually a bastardisation of an earlier, more vulgar and direct term which was slang for doing something very much the wrong way, as in "you are fucking the dog!" At Yale a friend of Rawlings', the radio DJ Jack May (a.k.a. "Candied Yam Jackson") amended this term to "screwing the pooch" which was simultaneously less vulgar and more pleasing to the ear.

The term, however, did not enter the popular lexicon until Tom Wolfe used it in his book about the space program "The Right Stuff" where is was used to describe a supposed mistake by astronaut Gus Grissom.

http://en.wiktionary.org/wiki/screw_the_pooch