The Collaborative International Dictionary of English v.0.48:

Inconsistency \In`con*sist"en*cy\, n.; pl. Inconsistencies.
   [Cf. F. inconsistance.]
   [1913 Webster]
   1. The quality or state of being inconsistent; discordance in
      respect to sentiment or action; such contrariety between
      two things that both can not exist or be true together;
      disagreement; incompatibility.
      [1913 Webster]

            There is a perfect inconsistency between that which
            is of debt and that which is of free gift. --South.
      [1913 Webster]

   2. Absurdity in argument ore narration; incoherence or
      irreconcilability in the parts of a statement, argument,
      or narration; that which is inconsistent.
      [1913 Webster]

            If a man would register all his opinions upon love,
            politics, religion, and learning, what a bundle of
            inconsistencies and contradictions would appear at
            last!                                 --Swift.
      [1913 Webster]

   3. Lack of stability or uniformity; unsteadiness;
      changeableness; variableness.
      [1913 Webster]

            Mutability of temper, and inconsistency with
            ourselves, is the greatest weakness of human nature.
                                                  --Addison.
      [1913 Webster]

WordNet (r) 3.0 (2006):

inconsistency
    n 1: the relation between propositions that cannot both be true
         at the same time [syn: incompatibility, mutual
         exclusiveness, inconsistency, repugnance]
    2: the quality of being inconsistent and lacking a harmonious
       uniformity among things or parts [ant: consistence,
       consistency]

Moby Thesaurus II by Grady Ward, 1.0:

175 Moby Thesaurus words for "inconsistency":
   aloofness, ambiguity, ambivalence, anarchy, antagonism, antilogy,
   antinomy, antipathy, antithesis, asymmetry, capriciousness,
   changeability, changeableness, chaos, choppiness, clashing,
   collision, conflict, confrontation, confusion, contradiction,
   contradistinction, contraindication, contraposition, contrariety,
   contrast, counterposition, cross-purposes, dappleness, departure,
   desultoriness, deviability, deviation, difference, differentiation,
   diffusion, disaccord, disaccordance, disagreement, disconformity,
   discongruity, discontinuity, discordance, discrepancy,
   discreteness, disjunction, dislocation, disorder, disparity,
   dispersal, dispersion, disproportion, disproportionateness,
   dissent, dissimilarity, dissolution, dissonance, distinction,
   distinctness, divarication, divergence, divergency,
   diversification, diversity, eccentricity, entropy, equivocality,
   erraticism, far cry, fickleness, flightiness, freakishness, heresy,
   heterodoxy, heterogeneity, hostility, illogic, illogicality,
   illogicalness, impulsiveness, inaccordance, incoherence,
   incommensurability, incompatibility, inconclusiveness, incongruity,
   inconsonance, inconstancy, inequality, inharmoniousness, inharmony,
   inimicalness, instability, invalidity, irrationality,
   irreconcilability, irregularity, jerkiness, mercuriality, mixture,
   moodiness, motleyness, mutability, nonadhesion, noncohesion,
   noncompliance, nonconcurrence, nonconformability, nonconformance,
   nonconformism, nonconformity, nonobservance, nonstandardization,
   nonuniformity, odds, oppositeness, opposition, opposure,
   oppugnance, oppugnancy, originality, otherness, oxymoron, paradox,
   perversity, pluralism, polarity, protest, raggedness,
   reasonlessness, recalcitrance, recusance, recusancy,
   refractoriness, repugnance, restlessness, scattering,
   self-contradiction, senselessness, separateness, shiftiness,
   showdown, unadherence, unadhesiveness, uncertainty,
   unconformability, unconformism, unconformity, undependability,
   unevenness, unfixedness, unlikeness, unorthodoxy, unpredictability,
   unreasonableness, unreliability, unscientificness, unsettledness,
   unsoundness, unstableness, unsteadfastness, unsteadiness,
   untenableness, untenacity, variability, variance, variation,
   variegation, variety, variousness, versatility, wantonness,
   wavering, waywardness, whimsicality