The Collaborative International Dictionary of English v.0.48:

Indelicacy \In*del"i*ca*cy\, n.; pl. Indelicacies. [From
   Indelicate.]
   The quality of being indelicate; lack of delicacy, or of a
   nice sense of, or regard for, purity, propriety, or
   refinement in manners, language, etc.; rudeness; coarseness;
   also, that which is offensive to refined taste or purity of
   mind.
   [1913 Webster]

         The indelicacy of English comedy.        --Blair.
   [1913 Webster]

         Your papers would be chargeable with worse than
         indelicacy; they would be immoral.       --Addison.
   [1913 Webster]

WordNet (r) 3.0 (2006):

indelicacy
    n 1: the trait of being indelicate and offensive
    2: an impolite act or expression