To vet was originally a horse-racing term, referring to the requirement that a horse be checked for health and soundness by a veterinarian before being allowed to race. Thus, it has taken the general meaning "to check".[2]
It is a figurative contraction of veterinarian, which originated in the mid-17th century. The colloquial abbreviation dates to the 1860s; the verb form of the word, meaning "to treat an animal", came a few decades later—according to the Oxford English Dictionary, the earliest known usage is 1891[3]—and was applied primarily in a horse-racing context ("He vetted the stallion before the race", "You should vet that horse before he races", etc.).
By the early 1900s, vet had begun to be used as a synonym for evaluate, especially in the context of searching for flaws