The Collaborative International Dictionary of English v.0.48:

Mustiness \Mus"ti*ness\, n.
   The quality or state of being musty.
   [1913 Webster]

WordNet (r) 3.0 (2006):

mustiness
    n 1: the quality of smelling or tasting old or stale or mouldy
         [syn: mustiness, must, moldiness]

Moby Thesaurus II by Grady Ward, 1.0:

38 Moby Thesaurus words for "mustiness":
   banality, banalness, cliche, commonness, commonplaceness,
   corniness, familiarness, fetidity, fetidness, foulness, frowst,
   frowstiness, frowziness, funkiness, fustiness, hackneyedness,
   malodorousness, mildew, moldiness, must, noisomeness, odorousness,
   offensiveness, platitudinousness, putridness, rancidity,
   rancidness, rankness, reastiness, repulsiveness, rottenness,
   smelliness, squareness, staleness, stinkingness, stuffiness,
   triteness, unoriginality