I recently bought Cattin' with John Coltrane and Paul Quinichette and wondered if there was something wrong with my copy when I heard clicking sounds. Then I realised they only occurred when Q was playing, so I suppose what I'm hearing is the mechanism of the horn.
This brought to mind a discussion here on Art Taylor's squeaking hi-hat. Then I thought of the mysterious clunks on Monk's recordings - there's one on his solo on "Pannonica" from Brilliant Corners IIRC. I remember reading that this was the sound of his hand hitting the wood of the piano, Monk's contortions while playing being as unorthodox as the sound he produced!
As for another sort of "noises off", I recall that on Chico Hamilton's "Walking Carson Blues" distant motor horns can be heard behind Carson Smith's (very quiet) bass solo. Someone told me there's a Billy Holliday recording at an open air festival where a plane can be heard flying over - a turboprop, he said! I've never heard this one though.
Discussing all this with Tom 1960 on Skype yesterday, he said that glasses and a cash register can be heard on the Shelly Manne at the Black Hawk sessions, though I don't remember noticing these. What I do recall is Mingus asking an imagined audience to avoid these sounds on his Candid studio session with Eric Dolphy, Ted Curson and Danny Richmond
I'd be pleased to have confirmation/correction of what I've written as well as hearing about noises off you've noticed. Of course, there may already be a thread on this ...