The Collaborative International Dictionary of English v.0.48:

Peculiarity \Pe*cul`iar"i*ty\ (p[-e]*k[=u]l`y[a^]r"[i^]*t[y^]),
   n.; pl. Peculiarities (p[-e]*k[=u]l`y[a^]r"[i^]*t[i^]z).
   1. The quality or state of being peculiar; individuality;
      singularity. --Swift.
      [1913 Webster]

   2. That which is peculiar; a special and distinctive
      characteristic or habit; particularity.
      [1913 Webster]

            The smallest peculiarity of temper or manner.
                                                  --Macaulay.
      [1913 Webster]

   3. Exclusive possession or right. [Obs.] --Bp. Hall.
      [1913 Webster]

WordNet (r) 3.0 (2006):

peculiarity
    n 1: an odd or unusual characteristic [syn: peculiarity,
         distinctive feature, distinguishing characteristic]
    2: a distinguishing trait [syn: peculiarity, specialness,
       specialty, speciality, distinctiveness]
    3: something unusual -- perhaps worthy of collecting [syn:
       curio, curiosity, oddity, oddment, peculiarity,
       rarity]

Moby Thesaurus II by Grady Ward, 1.0:

170 Moby Thesaurus words for "peculiarity":
   aberration, abnormality, absurdity, affectation, affection,
   anomaly, anticness, aroma, attribute, automatism, bad habit, badge,
   banner, bizarreness, bizarrerie, brand, cachet, caprice, cast,
   character, characteristic, command of language, conceit,
   configuration, crackpotism, crank, crankiness, crankism,
   creature of habit, crotchet, crotchetiness, curiousness, custom,
   cut, deformity, deviancy, deviation, device, differentia,
   differential, differentness, distinctive feature, divergence,
   dottiness, earmark, eccentricity, erraticism, erraticness,
   exaggeration, expression of ideas, fantasticality, fashion,
   feature, feeling for words, figure, flavor, force of habit,
   form of speech, freakiness, freakishness, grace of expression,
   grandiloquence, grotesqueness, grotesquerie, gust, habit,
   habit pattern, habitude, hallmark, idiocrasy, idiosyncrasy, image,
   impress, impression, index, indicant, indicator, individualism,
   inflation, insignia, irregularity, keynote, kink, lineaments,
   literary style, maggot, malformation, manner, manner of speaking,
   mannerism, mark, marking, measure, minauderie, mode,
   mode of expression, mold, monstrosity, monstrousness, nature,
   nonconformity, note, oddity, odor, outlandishness, particularity,
   pattern, peculiar trait, personal style, picture, practice, praxis,
   property, quaintness, quality, queerness, quip, quirk, quirkiness,
   representation, representative, rhetoric, savor, seal,
   second nature, sense of language, shape, sigil, sign, signal,
   signature, singularity, smack, speciality, specialty, stamp,
   stereotype, stereotyped behavior, strain, strangeness, style,
   stylistic analysis, stylistics, sure sign, symptom, taint, tang,
   taste, telltale sign, teratism, the grand style, the plain style,
   the sublime, token, trademark, trait, trick, trick of behavior,
   twist, unconventionality, unnaturalness, usage, use, vein, way,
   weirdness, whim, whimsicality, whimsy, wont