The Collaborative International Dictionary of English v.0.48:

Irregularity \Ir*reg`u*lar"i*ty\, n.; pl. Irregularities. [Cf.
   F. irr['e]gularit['e].]
   The state or quality of being irregular; that which is
   irregular.
   [1913 Webster]

WordNet (r) 3.0 (2006):

irregularity
    n 1: behavior that breaches the rule or etiquette or custom or
         morality [syn: abnormality, irregularity]
    2: not characterized by a fixed principle or rate; at irregular
       intervals [syn: irregularity, unregularity] [ant:
       regularity]
    3: an irregular asymmetry in shape; an irregular spatial pattern
       [syn: irregularity, geometrical irregularity]
    4: irregular and infrequent or difficult evacuation of the
       bowels; can be a symptom of intestinal obstruction or
       diverticulitis [syn: constipation, irregularity]

Moby Thesaurus II by Grady Ward, 1.0:

248 Moby Thesaurus words for "irregularity":
   Bohemianism, aberrance, aberrancy, aberration, abnormality,
   abnormity, affability, amorphism, anamorphism, anamorphosis,
   anomalism, anomalousness, anomaly, asperity, asymmetry,
   broken thread, brokenness, buckle, bumpiness, capriciousness,
   cardialgia, casualness, changeability, changeableness,
   cholera morbus, choppiness, colic, common touch, conceit,
   constipation, contortion, contrariety, cordiality, costiveness,
   crackpotism, cragginess, crank, crankiness, crankism, crookedness,
   crotchet, crotchetiness, dappleness, derangement, desultoriness,
   detorsion, deviability, deviancy, deviation, diarrhea, difference,
   differentiation, differentness, disarrangement, disarray,
   disarticulation, discomfiture, discomposure, disconcertedness,
   disconnectedness, disconnection, discontinuance, discontinuation,
   discontinuity, discontinuousness, discreteness, disequilibrium,
   disharmony, dishevelment, disintegration, disjunction, disorder,
   disorderliness, disorganization, disparity, disproportion,
   disruption, distortion, disturbance, divarication, divergence,
   diversification, dottiness, dysentery, dyspepsia, ease, easiness,
   easygoingness, eccentricity, entropy, episode, erraticism,
   erraticness, familiarity, fickleness, fitfulness, flightiness,
   flux, folksiness, freakiness, freakishness, gnarl, graciousness,
   granulation, gripe, gripes, haphazardness, harshness, heartburn,
   heterogeneity, heteromorphism, hispidity, homeliness, homeyness,
   idiocrasy, idiosyncrasy, imbalance, impulsiveness, inadequacy,
   incoherence, incompleteness, inconsistency, inconstancy,
   indigestion, indiscriminateness, inequality, inequity, inferiority,
   informality, informalness, inharmonious harmony, injustice,
   instability, insufficiency, intermittence, jaggedness, jerkiness,
   joltiness, kink, knot, lientery, looseness, lopsidedness, maggot,
   mannerism, mercuriality, monstrosity, moodiness,
   most admired disorder, motleyness, mutability, naturalness,
   non sequitur, nonconformism, nonconformity, noncontinuance,
   nonlinearity, nonseriality, nonstandardization, nonsymmetry,
   nonuniformity, obstipation, oddity, odds, offhandedness,
   overbalance, parenthesis, peculiarity, perturbation, plainness,
   pluralism, promiscuity, promiscuousness, pyrosis, queerness, quip,
   quirk, quirkiness, raggedness, randomness, relaxedness,
   restlessness, rough air, roughness, ruggedness, rugosity,
   scraggliness, screw, shiftiness, shortcoming, simplicity,
   singularity, sociability, strangeness, subnormality, superiority,
   teratism, tooth, torsion, tortuosity, trick, trots, turbulence,
   turn, twist, unaffectedness, unbalance, unceremoniousness,
   uncertainty, unconformism, unconformity, unconstrainedness,
   unconstraint, unconventionality, undependability, unevenness,
   unfair discrimination, unfixedness, unnaturalism, unnaturalness,
   unorthodoxy, unpredictability, unpretentiousness, unreliability,
   unsettledness, unsmoothness, unstableness, unsteadfastness,
   unsteadiness, unsymmetry, ununiformity, upset, variability,
   variation, variegation, variety, variousness, versatility,
   wantonness, warp, wavering, waywardness, whim, whimsicality,
   whimsy, wrench, wrest, wring



Bouvier's Law Dictionary, Revised 6th Ed (1856):

IRREGULARITY, practice. The doing or not doing that in the conduct of a suit
at law, which, conformably with the practice of the court, ought or ought
not to be done.
     2. A party entitled to complain of irregularity, should except to it
previously to taking any step by him in the cause; Lofft. 323, 333; because
the taking of any such step is a waiver of any irregularity. 1 Bos. k Phil.
342; 2 Smith's R. 391; 1 Taunt. R. 58; 2 Taunt. R. 243; 3 East, R. 547; 2
New R. 509; 2 Wils. R. 380.
     3. The court will, on motion, set aside proceedings for irregularity.
On setting aside a judgment and execution for irregularity, they have power
to impose terms on the defendant, and will restrain him from bringing an
action of trespass, unless a strong case of damage appears. 1 Chit. R. 133,
n.; and see Baldw. R. 246. Vide 3 Chit. Pr. 509; and Regular and Irregular
Process.
     4. In the canon law, this term is used to signify any impediment which
prevents a man from taking holy orders.