The late John Yeoman sent me a fine collection of short fiction set in Tudor England a couple of years ago, and far more the expert in the era of Shakespeare, Marlowe, and Webster than I could ever hope to be, his stories were replete with historical detail.
But, as I said to Dr Yeoman at the time - the idea, for instance, of a man eating Spanish oranges in London when Queen Liz the First was on the throne - had me looking to Wikipedia to peruse the history of the fruit.
By the way, this (highly recommended) collection and other work featuring his detective hero can be found at his Amazon author page.
But about the semblance of accuracy: In one of my own stories (set in 1906), a schoolboy called Jeremy is nicknamed Jez. Somebody said it seemed a little modern.
We do have Dickens's Boz, pre-dating "Jez" by half a century.
Anyway, the late great John Yeoman had himself edited that particular story after I had voiced some concerns to him about it - and he didn't mind these little things.
One edit I had paid serious attention to from another beta-reader was the relationships between staff and gentry. The fact is, the staff NEVER talked to the nobility the way they do in these Downton Abbey programmes. So in my yarn, I toned down the familiarity between the butler-maid couple and the civil servant for whom they worked.
Perhaps the semblance of historical accuracy gets a pass under a number of circumstances:
-if the author (such as Doc Yeoman above) knows better than the reader (if it jars a little for anyone, it's something that can be looked at)
-poetic licence (for a movie example, think Sofia Coppola's rendering of Marie Antoinette, or elsewhere, whether you can install mechanical elevators in Ancient Egypt, or at the wall holding back the Wildlings (for a fantasy example), or if there were battery-operated devices in pre-Muslim Mesopotamia)
-finally, importantly, does it work for the reader? (Again, some people didn't like Sofia Coppola's take, to cite this example)
A fish lifting its head off the plate to deliver its thoughts before a character tucks into it might suit the magic surrealist writings of Etger Keret. But it can be confidently dropped from your thriller about killing Hitler, unless (of course) the narrator is drugged and it's that kind of book.
Given that there are as many interpretations as there are readers, accuracy is a risk that every author and artist regularly runs.