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