Doesn't matter what is correct or what correct is?
When we're asking a question we use a reversed order of words:
Where is he?
When we're stating something we're using the normal order:
I don't know where he is.
But what about one?
It doesn't matter what is correct - if enough people make that mistake it stops being a mistake anymore.
Above I see the reversed order. Or maybe it just appears that way? At the moment of writing this I'm realizing that maybe it's not the case here since it's a verb-adjective pair instead of a verb-noun pair?
But anyway, maybe the alternative is correct then?
It doesn't matter what correct is - if enough people make that mistake it stops being a mistake anymore.
The alternative most certainly isn't correct, and your realization about comparing a verb-adjective to a verb-noun pair is correct.
In the second example, the pair ought to be highlighted as "It doesn't matter what is correct", and the word order is preserved.