The Collaborative International Dictionary of English v.0.48:

Impertinence \Im*per"ti*nence\, n. [Cf. F. impertinence. See
   Impertinent.]
   1. The condition or quality of being impertinent; absence of
      pertinence, or of adaptedness; irrelevance; unfitness.
      [1913 Webster]

   2. Conduct or language unbecoming the person, the society, or
      the circumstances; rudeness; incivility.
      [1913 Webster]

            We should avoid the vexation and impertinence of
            pedants who affect to talk in a language not to be
            understood.                           --Swift.
      [1913 Webster]

   3. That which is impertinent; a thing out of place, or of no
      value.
      [1913 Webster]

            There are many subtile impertinences learned in
            schools.                              --Watts.
      [1913 Webster]

WordNet (r) 3.0 (2006):

impertinence
    n 1: an impudent statement [syn: impudence, cheek,
         impertinence]
    2: the trait of being rude and impertinent; inclined to take
       liberties [syn: crust, gall, impertinence, impudence,
       insolence, cheekiness, freshness]
    3: inappropriate playfulness [syn: impertinence, perkiness,
       pertness, sauciness, archness]

Moby Thesaurus II by Grady Ward, 1.0:

73 Moby Thesaurus words for "impertinence":
   arrogance, audacity, bold front, boldness, brash bearing,
   brashness, brass, brassiness, bravado, brazenfacedness, brazenness,
   bumptiousness, butting-in, cheek, cheekiness, chutzpah, cockiness,
   contempt, contemptuousness, daring, daringness, defial, defiance,
   defying, derision, despite, disassociation, disconnection,
   discourtesy, discreteness, disdain, disjunction, disjuncture,
   disregard, disrespect, disrespectfulness, dissociation, effrontery,
   face of brass, flippancy, forwardness, freshness, gall, hardihood,
   immateriality, impoliteness, impudence, inapplicability,
   inappositeness, incivility, inconnection, inconsequence,
   independence, inquisitiveness, insolence, intermeddling,
   intrusiveness, irrelation, irrelevance, meddlesomeness, meddling,
   nerve, obtrusiveness, officiousness, pertness, presumption,
   presumptuousness, ridicule, rudeness, sauciness, separateness,
   unconnectedness, unrelatedness