The Collaborative International Dictionary of English v.0.48:

Tasteless \Taste"less\, a.
   1. Having no taste; insipid; flat; as, tasteless fruit.
      [1913 Webster]

   2. Destitute of the sense of taste; or of good taste; as, a
      tasteless age. --Orrery.
      [1913 Webster]

   3. Not in accordance with good taste; as, a tasteless
      arrangement of drapery; a tasteless remark.
      [1913 Webster] -- Taste"less*ly, adv. --
      Taste"less*ness, n.
      [1913 Webster]

WordNet (r) 3.0 (2006):

tastelessness
    n 1: the property of having no flavor [syn: flavorlessness,
         flavourlessness, savorlessness, savourlessness,
         tastelessness]
    2: inelegance indicated by a lack of good taste [ant:
       tastefulness]