The Collaborative International Dictionary of English v.0.48:

Musty \Mus"ty\, a. [Compar. Mustier; superl. Mustiest.]
   [From L. mustum must; or perh. fr. E. moist. Cf. Must, n.,
   Moist.]
   1. Having the rank, pungent, offensive odor and taste which
      substances of organic origin acquire during warm, moist
      weather; foul or sour and fetid; moldy; as, musty corn;
      musty books. --Harvey.
      [1913 Webster]

   2. Spoiled by age; rank; stale.
      [1913 Webster]

            The proverb is somewhat musty.        --Shak.
      [1913 Webster]

   3. Dull; heavy; spiritless. "That he may not grow musty and
      unfit for conversation." --Addison.
      [1913 Webster]

WordNet (r) 3.0 (2006):

musty
    adj 1: covered with or smelling of mold; "moldy bread"; "a moldy
           (or musty) odor" [syn: moldy, mouldy, musty]
    2: stale and unclean smelling [syn: fusty, musty, frowsty]

Moby Thesaurus II by Grady Ward, 1.0:

134 Moby Thesaurus words for "musty":
   ancient, antediluvian, antiquated, archaic, back-number, bad,
   bad-smelling, banal, bewhiskered, blasted, blighted, blown,
   bromidic, burning, bygone, cliched, common, commonplace, corny,
   crumbling, cut-and-dried, damp, decayed, despoiled, dilapidated,
   dirty, dusty, estral, estrous, estrual, fade, familiar, fecal,
   fetid, filthy, flyblown, foul, frowsty, frowsy, frowy, frowzy,
   fulsome, funky, fusty, gamy, gone to seed, graveolent, hackney,
   hackneyed, high, hoary, hot, ill-smelling, in heat, in must,
   in rut, maggoty, malodorous, mephitic, miasmal, miasmic, mildewed,
   mildewy, moldering, moldy, moss-grown, moth-eaten, mouldy, must,
   nidorous, noisome, noxious, obsolete, odorous, offensive, old hat,
   old-fashioned, olid, out of date, passe, platitudinous, putrid,
   rancid, rank, ravaged, reasty, reasy, reechy, reeking, reeky,
   repulsive, rotten, ruined, ruinous, rusty, rutting, ruttish, rutty,
   set, shopworn, smellful, smelling, smelly, smutted, smutty, sour,
   spoilt, squalid, square, stale, stenchy, stereotyped, stinking,
   stock, strong, stuffy, sulfurous, threadbare, time-scarred,
   timeworn, tired, trite, truistic, unoriginal, vile, warmed-over,
   weevily, well-known, well-worn, worm-eaten, wormy, worn, worn out,
   worn thin