The New York Times magazine has a clever piece by a former New Yorker fact checker, the person charged with verifying every factual point in their articles. A longer, more detailed description of the magazine's process is, regrettably, behind a subscription firewall. I've read that only a few publications like The New Yorker and The Atlantic still devote significant resources to fact checking -- for which we can all feel cheated, since so many errors become "facts" once published and Googled.
I draw attention to these articles because I have had two quite different experiences in fact checking. I've now written four books published by three different publishers -- and at no time in the editorial process was I aware of any attempt at fact checking what appeared, bound for eternity, in a printed book. I'm told that is not unusual. Lawyers may review manuscripts, but rarely people trying to verify statements.
On the other hand, The New Yorker ran a series of articles about my then boss in the 1970s, Senator John Culver [D-Iowa], and I was one of many recipients of quite detailed questions from the magazine's legendary fact checkers. "Do you wear rimless glasses?" one asked. "Well, there's wire around the top but not underneath the lenses," I replied, trying to be precise. "What's the color of the rug in Senator Culver's office?" I called the staffer sitting just outside. He looked in and told me, "I'd call it cat puke pink." The magazine used different terminology, but I thereafter always viewed New Yorker facts as the gold standard in accuracy.