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]