...you're using "dialect" as a class-based division rather than a geographical one.
As I said, it is very complicated. It is geographical, but it is also due to education, gender, age, ethnicity, and other social variables. I would guess that even in the early Twentieth Century a tenant farmer spoke a different accent to the landowner despite being born yards away from each other.
...to my mind again points to its being incorrect usage of standard English, not a hangover from a time when it was considered to be correct in anyone's tongue in any area or social class.
By "Standard" English", I'm assuming you are using the definition of the "language variety used by a population for public purposes." There are 'Received Pronunciation' or 'Queen's English' which were taught in the early Twentieth Century in England and spoken on the BBC, but that was not the way the vast majority of the population ever spoke. To imply the vast majority of the population speaks incorrectly because of their "class" still irks me.
You may be correct that this use of "what" isn't geographical. I have no evidence except that it is impossible to wipe out similar kinds of regional difference in language even with compulsory education. The Chinese have been trying to enforce Mandarin for many years and have not yet succeeded.
Am I taking a throwaway comment a little too personally? Yes, probably, but like the other anecdotes regarding dialects already given here, I was ribbed for several years because, rather than say, "I'm going to take a shower," or, "I'm going to have a shower," I would say, "I'm going to get a shower." My friend would ask if I really hadn't bought enough showers yet? However, my word construction was not wrong or incorrect, it was just a product of my own regional dialect together with my own education, gender, age, ethnicity, and social variables (including "class" if such a thing still exists.) At junior school I was also ribbed because I pronounced "Film" as "Filim" but I've since come to realise that too is just an extremely localised case of dialect differences because of social variables. At university, people would knock on my door and ask me to pronounce "Road" which is even funnier now, because back in the North East I would now be considered a Southerner from the way I speak.
My pronunciation of words and my sentence construction represents "me" personally; it is a part of who I am, and as
@Ursa major points out, it includes my heritage and ethnicity just as much as location of birth.