The Collaborative International Dictionary of English v.0.48:

Sordidness \Sor"did*ness\, n.
   The quality or state of being sordid.
   [1913 Webster]

WordNet (r) 3.0 (2006):

sordidness
    n 1: sordid dirtiness [syn: sordidness, squalor,
         squalidness]
    2: unworthiness by virtue of lacking higher values [syn:
       baseness, sordidness, contemptibility,
       despicableness, despicability]