A legal officer referred to a claimant’s claims and evidence as vague and inconsistent (which is not unusual) but also as containing significant vagary and inconsistency.
By itself it is possible for claims and evidence to contain significant vagary:
1. an unpredictable or erratic action, occurrence, course, or instance
2. a whimsical, wild, or unusual idea, desire, or action
but the closest noun equivalent of vague is vagueness. In fact, Dictionary.com doesn’t have a separate definition for vagueness, redirecting searches for it to the definition for vague. Vagary may at one time have been the best equivalent for vague, but it isn’t now. –ness is a very common and productive noun morpheme. Also, vagaries is much more commonly used than vagary.
We most often talk or write about (a/the/-) vague idea(s), sense, feeling, notion(s), term(s), way, hope (they are mostly internal), (a/the) vagary of nature, thought, fashion, fate, fortune/Fortune, imagination, taste, mine, fancy and vagaries of life, nature, weather, chance, climate, fortune, fashion, politics, fancy, imagination (they are mostly external).
But vague/vagueness and vagary share an origin in Latin vagus, wandering, vagārī to wander (compare vagrant/vagrancy).