The Collaborative International Dictionary of English v.0.48:

Incompatibility \In`com*pat`i*bil"i*ty\, n.; pl. -ties. [Cf.
   F. incompatibilit['e].]
   The quality or state of being incompatible; inconsistency;
   irreconcilableness.
   [1913 Webster]

WordNet (r) 3.0 (2006):

incompatibility
    n 1: the relation between propositions that cannot both be true
         at the same time [syn: incompatibility, mutual
         exclusiveness, inconsistency, repugnance]
    2: (immunology) the degree to which the body's immune system
       will try to reject foreign material (as transfused blood or
       transplanted tissue)
    3: the quality of being unable to exist or work in congenial
       combination [ant: compatibility]

The Devil's Dictionary (1881-1906):

INCOMPATIBILITY, n.  In matrimony a similarity of tastes, particularly
the taste for domination.  Incompatibility may, however, consist of a
meek-eyed matron living just around the corner.  It has even been
known to wear a moustache.