While searching for the etymology of the phrase asleep at the switch, I found this marvellous Idler's Glossary. It didn't tell me the answer, of course: that's in Brewer's, which is where I should have looked in the first place:
Asleep at the switch, To be. To fail to attend to one's duty; to be unvigilant. An American expression derived from the railroads. `To switch a train' is to transfer it to another set of rails by operating a switch. Failure to do this according to schedule might well lead to a catastrophe.
Still no news on screw the pooch, which Brewer's doesn't cover (and neither does the OED). A Google search for "screw the pooch" etymology doesn't get us very far, sadly. The phrase occurs in a bunch of dictionaries of military and naval terminology, and also in dictionaries of jazz terms -- bizarre. (Have a look at OneLook, which is some sort of meta-dictionary-search, which of itself looks quite useful, though it doesn't help much here.) Perhaps I need a better dictionary of slang.