In·del·i·ca·cy n.; pl. Indelicacies 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.
The indelicacy of English comedy. --Blair.
Your papers would be chargeable with worse than indelicacy; they would be immoral. --Addison.
n 1: the trait of being indelicate and offensive
2: an impolite act or expression