The Collaborative International Dictionary of English v.0.48:

Incompetence \In*com"pe*tence\, Incompetency \In*com"pe*tency\,
   n. [Cf. F. incomp['e]tence.]
   [1913 Webster]
   1. The quality or state of being incompetent; lack of
      physical, intellectual, or moral ability; lack of
      qualifications or training (for a particular task);
      insufficiency; inadequacy; as, the incompetency of a child
      for hard labor, or of an idiot for intellectual efforts.
      "Some inherent incompetency." --Gladstone.

   Syn: incompetence.
        [1913 Webster]

   2. (Law) Lack of competency or legal fitness; incapacity;
      disqualification, as of a person to be heard as a witness,
      or to act as a juror, or of a judge to try a cause.

   Syn: Inability; insufficiency; inadequacy; disqualification;
        incapability; unfitness.
        [1913 Webster]

WordNet (r) 3.0 (2006):

incompetence
    n 1: lack of physical or intellectual ability or qualifications
         [syn: incompetence, incompetency] [ant: competence,
         competency]
    2: inability of a part or organ to function properly

Moby Thesaurus II by Grady Ward, 1.0:

84 Moby Thesaurus words for "incompetence":
   ad lib, baseness, deficiency, disability, disablement,
   disqualification, extemporaneousness, failure, falling short,
   faultiness, fewness, imbecility, imperfection, improvisation,
   inability, inadeptness, inadequacy, inadequateness, inaptitude,
   inaptness, inattentiveness, incapability, incapacitation,
   incapacity, incompetency, indexterity, ineffectiveness,
   ineffectuality, inefficiency, ineptitude, ineptness, infancy,
   inferiority, insufficiency, insufficientness, lack of preparation,
   legal incapacity, littleness, maladjustment, maladroitness,
   meanness, mediocrity, minority, none to spare, nonfulfillment,
   nonpreparation, nonpreparedness, nonsatisfaction, pedestrianism,
   pettiness, planlessness, rustiness, shabbiness, short supply,
   skill-lessness, smallness, subnormality, thoughtlessness, too late,
   too little, triviality, unaptness, uncleverness, undeftness,
   undexterousness, undextrousness, unfitness, unfittedness,
   unintelligence, unpreparedness, unproficiency, unqualification,
   unqualifiedness, unreadiness, unschooledness, unskillfulness,
   unsuitability, unsuitableness, unsuitedness, untrainedness,
   uselessness, vulgarity, vulnerability, wardship