The Collaborative International Dictionary of English v.0.48:

Seediness \Seed`i*ness\, n.
   The quality or state of being seedy, shabby, or worn out; a
   state of wretchedness or exhaustion. [Colloq.] --G. Eliot.
   [1913 Webster]

         What is called seediness, after a debauch, is a plain
         proof that nature has been outraged.     --J. S.
                                                  Blackie.
   [1913 Webster]

WordNet (r) 3.0 (2006):

seediness
    n 1: a lack of elegance as a consequence of wearing threadbare
         or dirty clothing [syn: shabbiness, seediness,
         manginess, sleaziness]