I think that the passage of time has probably diluted some of the way in which Mencken depicted Southerners in his essay, but some of those elements are still present in how the South is viewed today. The common caricature of the South is one where a lack of education is evident. The backwoods, "White trash," hillbilly is still a construction regarding the depiction of Southerners. In this, one can find some resonance in the items that Mencken brings out in his essay:
In all that gargantuan paradise of the fourth-rate there is not a single picture gallery worth going into, or a single orchestra capable of playing the nine symphonies of Beethoven, or a single opera-house, or a single theater devoted to decent plays, or a single public monument that is worth looking at, or a single workshop devoted to the making of beautiful things.
This is still a stereotype that exists to a lesser extent that the South is still filled with racists who live and perish off of NASCAR racing, comprised of people who say, "Git er done!" Mencken's assertion that the South "lacks all civilized culture" is still present in the standard depiction of the South today, albeit to a considerably less extent that his original intent.