The Collaborative International Dictionary of English v.0.48:

Incongruity \In`con*gru"i*ty\, n.; pl. Incongruities. [Pref.
   in- not + congruity: cf. F. incongruit['e].]
   [1913 Webster]
   1. The quality or state of being incongruous; lack of
      congruity; unsuitableness; inconsistency; impropriety.
      [1913 Webster]

            The fathers make use of this acknowledgment of the
            incongruity of images to the Deity, from thence to
            prove the incongruity of the worship of them. --Bp.
                                                  Stillingfleet.
      [1913 Webster]

   2. Disagreement of parts; lack of symmetry or of harmony.
      [Obs.]
      [1913 Webster]

   3. That which is incongruous; lack of congruity.
      [1913 Webster]

WordNet (r) 3.0 (2006):

incongruity
    n 1: the quality of disagreeing; being unsuitable and
         inappropriate [syn: incongruity, incongruousness] [ant:
         congruence, congruity, congruousness]