As we know, many English-speaking people use the labiodental /f/ and /v/ in place of intervocalic /θ/ and /ð/. This was at one time claimed to be a feature of Cockney, but it is far more widespread than that.
An interesting hypercorrection is to use /ð/ where standard English would have /v/. When this happens among people who would normally be considered well, or very well educated, does it warrant an entry in dictionaries as a variant, particularly if the hypercorrection appears in print?
I have recently read Sir Leonard Woolley’s book “Ur of the Chaldees”, first published in 1929. My copy is a Pelican Book, printed in 1938, and on page 140, we can read the sentence “Crushed together under a fallen brick we found at least a hundred slithers of ivory, many of them minute in size and as thin as tissue-paper.” As it happens, I also have a copy of the revised edition published in 1982 with “minimal revisions” by P R S Mooney, described on the fly leaf as “Senior Assistant Keeper in the Department of Antiquities, the Ashmolean Museum, Oxford”. The identical sentence, with no changes, appears on page 253. Previously, I have only heard this combination of pronunciation and meaning from people who, from their accent and other oral behaviour, could be assumed to be hypercorrecting.
The nearest OED definition of slither, as a noun, is “Something smooth and slippery; a smoothly sliding mass, the same as sliver n.1 1.”, where we have “A piece cut or split off; a long thin piece or slip; a splinter, shiver, slice”. I’m not sure whether this means that Oxford is, or is not, accepting “slither” as an alternative spelling to “sliver” in this sense. If they are, perhaps they should give at least one example sentence, and Woolley seems to provide the perfect one.