NOUN (2)

1. (Christianity) holding views that disagree with accepted doctrine; especially disagreement with papal infallibility;
- Example: "he denies the errancy of the Catholic Church"

2. fallibility as indicated by erring or a tendency to err;

The Collaborative International Dictionary of English v.0.48:

Errancy \Er"ran*cy\, n. [L. errantia.]
   A wandering; state of being in error.
   [1913 Webster]

WordNet (r) 3.0 (2006):

errancy
    n 1: (Christianity) holding views that disagree with accepted
         doctrine; especially disagreement with papal infallibility;
         "he denies the errancy of the Catholic Church"
    2: fallibility as indicated by erring or a tendency to err [ant:
       inerrancy]

Moby Thesaurus II by Grady Ward, 1.0:

40 Moby Thesaurus words for "errancy":
   aberrancy, aberration, defectiveness, delusion, deviancy,
   distortion, errability, erroneousness, error, fallaciousness,
   fallacy, fallibility, falseness, falsity, fault, faultiness, flaw,
   flawedness, hamartia, heresy, heterodoxy, illusion,
   liability to error, misapplication, misconstruction, misdoing,
   misfeasance, misinterpretation, misjudgment, peccancy, perversion,
   self-contradiction, sin, sinfulness, unorthodoxy, untrueness,
   untruth, untruthfulness, wrong, wrongness