The Collaborative International Dictionary of English v.0.48:

Insignificance \In`sig*nif"i*cance\, n.
   1. The condition or quality of being insignificant; lack of
      significance, sense, or meaning; as, the insignificance of
      words or phrases.
      [1913 Webster]

   2. Lack of force or effect; unimportance; pettiness;
      inefficacy; as, the insignificance of human art.
      [1913 Webster]

   3. Lack of claim to consideration or notice; lack of
      influence or standing; meanness.
      [1913 Webster]

            Reduce him, from being the first person in the
            nation, to a state of insignificance. --Beattie.
      [1913 Webster]

WordNet (r) 3.0 (2006):

insignificance
    n 1: the quality of having little or no significance [ant:
         significance]

Moby Thesaurus II by Grady Ward, 1.0:

53 Moby Thesaurus words for "insignificance":
   aimlessness, daintiness, dead letter, delicacy, diminutiveness,
   emptiness, empty sound, exiguity, exiguousness, fewness, futility,
   immateriality, inanity, inconsequence, inconsequentiality,
   inconsiderableness, indifference, ineffectuality, inferiority,
   insufficiency, irrelevance, littleness, low priority, marginality,
   meagerness, meaninglessness, meanness, mere noise, minuteness,
   moderateness, negligibility, noise, nonsensicality, nullity,
   pettiness, phatic communion, picayune, picayunishness, pokiness,
   puniness, purposelessness, scantiness, secondariness,
   senselessness, slightness, smallness, tininess, triviality,
   unimportance, unimpressiveness, unmeaningness, unnoteworthiness,
   unsignificancy