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

Moby Thesaurus II by Grady Ward, 1.0:

49 Moby Thesaurus words for "indelicacy":
   Babbittry, bad taste, boorishness, bourgeois taste, camp,
   campiness, churlishness, coarseness, crudeness, grossness,
   high camp, immodesty, impoliteness, impropriety, inappropriateness,
   incivility, indecency, indecorousness, indecorum, indiscreetness,
   indiscretion, inelegance, inelegancy, kitsch, low camp,
   offensiveness, philistinism, poor taste, pop, pop culture,
   roughness, rudeness, shamelessness, tastelessness, unaestheticism,
   unaestheticness, unbecomingness, unchastity, uncourtliness,
   unfittingness, unmannerliness, unrefinement, unseemliness,
   unsuitability, unsuitableness, vulgar taste, vulgarism, vulgarity,
   vulgarness