Verb, transitive. OED gives its first use as 1906 (in a Rudyard Kipling story), and defines it as, “To examine carefully and critically for deficiencies or errors; spec. to investigate the suitability of (a person) for a post that requires loyalty and trustworthiness.” It is so common now, and used in so many different contexts, that it probably doesn’t seem like a Britishism. But it is: a Google Ngram (for “vetting” and “vetted”) shows it starting to become popular in British English in the 1930s and peaking around 1990–exactly the same time, according to an Ngram for American English, that it started to take off in the U.S. Currently, it’s roughly equally popular on both sides of the ocean.
“If I was on a matchmaking site, I would want to know that the people they are going to hook me up with had at least been vetted.” (The Desert Sun, May 8, 2011)/Vetting for [Zoe] Baird’s appointment began at once. Exactly what her position might be was left unclear; the vetting team was simply told that it would be something important. (Sidney Blumenthal, The New Yorker, February 15, 1993)
notoneoffbritishisms.com 
If you’re short of new material for your blog, today’s New York Post headline rather suggests itself.
Sorted.
The word ‘vetted’ originally referred to having a horse checked out by a veterinarian prior to purchasing it. Still does. We talk about elections being horse races (and I adore the expression ‘a racing certainty’), so it’s not a far jump to having political candidates vetted as well.
One Britishism which does NOT make sense is ‘tarmac’ when used to refer to any airport runway, especially those made of concrete. Concrete is NOT tar-macadam.
Clearly, MAD will have to revisit this theme and point out the joke the media has played on the entire nation in its failure to properly vet Obama.
That’s vet (verb), what about Vet (noun) which in the UK means Veterinarian, not Veteran of war which we would refer to as ex-serviceman or old soldier.
I agree. When I was a small child my parents and I visited rellies in the USA. I asked my mother why they had sent a sick uncle to “the Vets'”, which I understood to mean “veterinarian”.
As she told me, the meant “the Veterans’ Hospital”.