The Collaborative International Dictionary of English v.0.48:

Inexpedience \In`ex*pe"di*ence\, Inexpediency
\In`ex*pe"di*en*cy\, n.
   The quality or state of being inexpedient; lack of fitness;
   unsuitableness to the end or object; impropriety; as, the
   inexpedience of some measures.
   [1913 Webster]

         It is not the rigor but the inexpediency of laws and
         acts of authority which makes them tyrannical. --Paley.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inexpedience
    n 1: the quality of being unsuited to the end in view [syn:
         inexpedience, inexpediency] [ant: expedience,
         expediency]

Moby Thesaurus II by Grady Ward, 1.0:

87 Moby Thesaurus words for "inexpedience":
   bad policy, badness, callowness, childishness, damnability,
   evilness, immaturity, impolicy, improperness, impropriety,
   imprudence, inaccuracy, inadvisability, inappropriateness,
   inattention, inauspiciousness, inconsideration, inconvenience,
   indiscreetness, indiscretion, inexpediency, infelicity,
   inferiority, injudiciousness, inopportuneness, inopportunity,
   intempestivity, interruption, intrusion, invalidity, irrationality,
   irrelevance, lateness, maladministration, malevolence, malfeasance,
   malpractice, misadministration, misconduct, misdirection,
   misfeasance, misgovernment, misguidance, mishandling,
   mismanagement, misrule, moral badness, neglect, negligence,
   nonfeasance, omission, peccancy, pompousness, prematurity,
   puerility, reasonlessness, recklessness, reprehensibility,
   senselessness, stuffiness, thoughtlessness, unfavorableness,
   unfitness, unfittingness, unfortunateness, unhealthiness,
   unintelligence, unkindness, unpleasantness, unpropitiousness,
   unreason, unreasonableness, unripeness, unseasonableness,
   unsensibleness, unskillfulness, unsoundness, unsuitability,
   unthoughtfulness, untimeliness, unwisdom, unwiseness, viciousness,
   wickedness, witlessness, wrongdoing, wrongness