The Collaborative International Dictionary of English v.0.48:

Unsound \Un*sound"\, a.
   Not sound; not whole; not solid; defective; infirm; diseased.
   [1913 Webster] -- Un*sound"ly, adv. -- Un*sound"ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

unsound
    adj 1: not in good condition; damaged or decayed; "an unsound
           foundation" [ant: sound]
    2: not sound financially; "unsound banking practices" [ant:
       sound]
    3: containing or based on a fallacy; "fallacious reasoning"; "an
       unsound argument" [syn: fallacious, unsound]
    4: suffering from severe mental illness; "of unsound mind" [syn:
       mentally ill, unsound, unstable]
    5: physically unsound or diseased; "has a bad back"; "a bad
       heart"; "bad teeth"; "an unsound limb"; "unsound teeth" [syn:
       bad, unfit, unsound]
    6: of e.g. advice

Moby Thesaurus II by Grady Ward, 1.0:

267 Moby Thesaurus words for "unsound":
   Albigensian, Arian, Catharist, Donatist, Ebionitist, Erastian,
   Gnostic, Jansenist, Jansenistic, Jovinianist, Jovinianistic,
   Lollard, Manichaean, Monophysite, Monophysitic, Montanist,
   Montanistic, Pelagian, Sabellian, Waldensian, Wyclifite, abnormal,
   adulterated, afflicted, ailing, antinomian, apocryphal, batty,
   bereft of reason, blemished, brainsick, broken-down, cachectic,
   chancy, crackbrained, cracked, crazed, crazy, crumbling, daft,
   damaged, dangerous, debilitated, decayed, decrepit, defective,
   deficient, delicate, deluded, demented, deprived of reason,
   deranged, desultory, dilapidated, diseased, disintegrating,
   disoriented, distraught, doubtful, drained, dubious, emanationist,
   enervated, erroneous, exhausted, failing, fallacious, fallible,
   faulty, feeble, flawed, flighty, flimsy, found wanting, fragile,
   frail, groundless, hairy, hallucinated, hazardous, healthless,
   heretical, heterodox, hylotheist, hylotheistic, ill, ill-advised,
   ill-considered, ill-contrived, ill-devised, ill-gauged, ill-judged,
   illogical, immature, impaired, imperfect, impolitic, imprecise,
   imprudent, impure, in poor health, inaccurate, inadequate,
   inadvisable, incomplete, inconclusive, inconsiderate, incorrect,
   indebted, indiscreet, inexact, inexpedient, infirm, injudicious,
   injured, insane, insecure, insensate, insolvent, insubstantial,
   invalid, irrational, jeopardous, lacking, languishing, loco,
   lunatic, mad, maddened, makeshift, manic, mazed, mediocre, mental,
   mentally deficient, meshuggah, mindless, misadvised, misguided,
   mixed, moon-struck, morbid, moribund, myopic, non compos,
   non compos mentis, nonorthodox, not all there, not perfect,
   not right, odd, of unsound mind, off, pale, pantheist, pantheistic,
   partial, patchy, pathological, peaked, peaky, perilous, poor,
   poorish, precarious, provisional, psycho, psychotic, queer,
   ramshackle, reasonless, reckless, reduced, reduced in health,
   rickety, risky, rocky, rotten, rotten at, run-down, senseless,
   shaky, shifting, shifty, short, shortsighted, sick, sickly,
   sketchy, slippery, specious, stark-mad, stark-staring mad, strange,
   temporary, tentative, tetched, thoughtless, ticklish, tottering,
   tottery, touched, treacherous, unaccepted, unadvised, unapproved,
   unauthentic, unauthoritative, unbalanced, uncanonical, uncertain,
   unconsidered, undependable, undeveloped, undiscerning, uneven,
   unfaithworthy, unfinished, unfirm, unforeseeing, unfounded,
   unhealthy, unhinged, unorthodox, unperfected, unpredictable,
   unproved, unreasonable, unreflecting, unreflective, unreliable,
   unrigorous, unsafe, unsane, unscriptural, unseeing, unsensible,
   unsettled, unsolid, unstable, unsteadfast, unsteady, unsturdy,
   unsubstantial, unsure, unsustained, untenable, unthinking,
   unthorough, unthoughtful, untrue, untrustworthy, unwell,
   unwholesome, unwise, valetudinarian, valetudinary, wandering, weak,
   weakened, weakly, wicked, with low resistance, witless, wobbly,
   wounded, wrong