The Collaborative International Dictionary of English v.0.48:

Nastiness \Nas"ti*ness\, n.
   The quality or state of being nasty; extreme filthness;
   dirtiness; also, indecency; obscenity.
   [1913 Webster]

         The nastiness of Plautus and Aristophanes. --Dryden.
   [1913 Webster]

WordNet (r) 3.0 (2006):

nastiness
    n 1: a state characterized by foul or disgusting dirt and refuse
         [syn: filth, filthiness, foulness, nastiness]
    2: malevolence by virtue of being malicious or spiteful or nasty
       [syn: cattiness, bitchiness, spite, spitefulness,
       nastiness]
    3: the quality of being unpleasant; "I flinched at the nastiness
       of his wound" [ant: niceness]