A delicious label. Below are some takes on What It Means, gathered via a Google search (and so neither exhaustive nor authoritative, but suggestive nonetheless):
A "Mouldy Fig" is a person who likes to play old jazz...I think it was Louis Armstrong who described academic jazz critics as "mouldy figs"...
Jazz term. A mouldy fig (or, for our American readers, a moldy fig) is a fellow who listens to and enjoys pre-bop jazz. Dixieland. Someone who’s not hip to the bop, you know?
What mouldy figdom... boils down to is the snooty, hipper-than-thou dismissal of anything remotely popular and/or new in music. Whatever the masses like couldn't possibly be good, and whatever's going on now was done better 30 years ago.
Leonard feather was credited with inventing the term and to emphasise the, to him, "old fashioned" style of the music he used to spell it "Mouldy Figge".
Anyone who listened to Dixieland jazz was at one time called a "mouldy-fig."
...the mouldy-fig fallacies of the gullible blues buff Samuel Charters and the sacrosanct amateur culture theorist LeRoi Jones...
If you want real figs.. try the Bix Board..
...his distinctive slur is very much a function of his unique vocal embouchure (he has a slight speech impediment). It offended rock critics--including me--not just because it seemed like a condescending mouldy-fig romanticization of the broken-down bluesman but because it wasn't forceful enough for rock and roll, as if he'd turned Junior Wells into John Hurt. I've never kept many of his records and suspect they still suffer from interpreter's disease--it's almost impossible to make every song new.
As the music pioneered by Dizzy Gillespie, Charlie Parker, and Bud Powell blossomed in the mid-1940s, non-musicians rigged a phony war between bebop and older jazz. As little wars often will, it got out of hand. A few jazz critics and elements of the general press promoted the idea that boppers and mouldy-fig traditionalists hated one another. It took years for the notion to dissipate.
And what I'm seeing, in the blue/newgrass community, is an even sharper divide, between traditionalists and modernists, than there is in jazz (where it's bad enough!). You have to really make sure you know people, before mentioning names like Bela Fleck -- otherwise you get a scowl. Someone in another thread was talking about the traditional bluegrass community being hurt by the fact that the best banjo player to come along in years left the idiom and made his own thing happen. That's what happened in jazz, and the "mouldy fig" dixieland crowd still hasn't accepted it, 50+ years later. I've played with a lot of trad-jazz guys who still denounce "that bebop crap" even today.
Charlie Jackson Mouldy Fig Stomp 1946 Musical Madness
Red Hot Jazz Archive (2000+ RealAudio examples of pre-1930 jazz...)