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):

incompetency
    n 1: lack of physical or intellectual ability or qualifications
         [syn: incompetence, incompetency] [ant: competence,
         competency]

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

INCOMPETENCY, evidence. The want of legal fitness, or ability in a witness
to be heard as such on the trial of a cause.
     2. The objections to the competency (q.v.) of a witness are four-fold.
The first ground is the want of understanding; a second is defect of
religious principles; a third arises from the conviction of certain crimes,
or infamy of character; the fourth is on account of interest. (q.v.) 1
Phil. Ev. 15.



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

INCOMPETENCY, French law. The state of a judge who cannot take cognizance of
a dispute brought before him; it implies a want of jurisdiction.
     2. Incompetency is material, ratione materia, or personal, ratione
personae. The first takes place when a judge takes cognizance of a matter
over which another judge has the sole jurisdiction, and this cannot be cured
by the appearance or agreement of the parties.
     3. The second is, when the matter in dispute is within the jurisdiction
of the judge, but the parties in the case are not; in which case they make
the judge competent, unless they make their objection before they. take
defence. See Peck, 374; 17 John. 13; 12 Conn. 88; 3 Cowen, Rep. 724; 1 Penn.
195; 4 Yeates, 446. When a party has a privilege which exempts him from the
jurisdiction, he may waive the privilege. 4 McCord, 79; Wright, 484; 4 Mass.
593; Pet. C. C. R. 489; 5 Cranch, 288; 1 Pet. R. 449; 4 W. C. C. R. 84; 8
Wheat. 699; Merl. Rep. mot Incompetence.
     4. It is a maxim in the common law, aliquis non debet esse judex in
propria causa. Co. Litt. 141, a; see 14 Vin. Abr. 573; 4 Com. Dig. 6. The
greatest delicacy, is constantly observed on the part of judges, so that
they never act when there could be the possibility of doubt whether they
could be free from bias, and even a distant degree of relationship has
induced a judge to decline interfering. 1 Knapp's Rep. 376. The slightest
degree of pecuniary interest is considered as an insuperable objection. But
at common law, interest forms the only ground for challenging a judge. It is
not a ground of challenge that he has given his opinion before. 4 Bin. 349;
2 Bin. 454. See 4 Mod. 226; Comb. 218; Hard. 44; Hob. 87; 2 Binn. R. 454; 13
Mass. R. 340; 5 Mass. R. 92; 6 Pick. 109; Peck, R. 374; Coxe, Rep. 190; 3
Ham. R. 289; 17 John. Rep. 133; 12 Conn. R. 88; 1 Penning R. 185; 4 Yeates,
R. 466; 3 Cowen, R. 725; Salk. 396; Bac. Ab. Courts, B; and the articles
Competency; Credibility; Interest; Judge; Witness.