The Collaborative International Dictionary of English v.0.48:

Inappropriate \In`ap*pro"pri*ate\, a.
   Not instrument (to); not appropriate; unbecoming; unsuitable;
   not specially fitted; -- followed by to or for. --
   In`ap*pro"pri*ate*ly, adv. -- In`ap*pro"pri*ate*ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inappropriateness
    n 1: inappropriate conduct [syn: inappropriateness,
         wrongness] [ant: appropriateness, rightness]
    2: the quality of being not particularly suitable or befitting;
       "he retracted nothing that he had said about the
       inappropriateness of either a corporeal God or a God who is a
       person"; "his praise released from her loud protestations of
       her unworthiness" [syn: inappropriateness, unworthiness]
       [ant: appropriateness]