Cascode,
Affectionately and with respect, I would venture a guess that you really lack a true breadth of observation for some of what you argue about US accents and dialects. You have been exposed to a much smaller pool of speakers than your average American who has lived there for decades. To that extent, I can sort of understand Mindy's frustration - she grew up there.
(as did I).
Particularly up to the second World War, the US population was not as mobile as it is today, and there were great differences between the English spoken say, in coastal South Carolina and that spoken in upstate New York.
I think my earlier point was that even within these discreet dialect regions, such as Virginia, my home state, natives (but admittedly perhaps not those from other parts of the US, or those from other countries) can hear the difference between their own local speech and that of people from an hour or so away.
Geographically, that means that the divisions are much larger than in the UK, where, as you point out, big differences sometimes exist between narrowly adjacent regions (Liverpool and Lancashire, just as one example).
However, and this is something the US has in common with the UK, there is a gradient not only of region, but also in social class. There are usually prestige forms and "lower" forms of local accents wherever you go in the US.
There are true dialects, or rather were, in the US, but there has been significant levelling due to mobility of the population and the rise of mass media in the 20th century. My sense is that local forms of English in the UK are more tenacious, but from the reading I have done on this topic, I believe there is also some levelling going on in this country as well.
I don't know how many times I have heard English people say Americans thought an English accent was what Dick van Dyke used in Mary Poppins. Those of us who actually live here probably have a greater level of linguistic sophistication on that score than your average tourist/visitor, though. Conversely, there aren't too many Brits who can convincingly do an American accent - one of my favourite examples of this malady is Dianna Troy on Star Trek. I think to really be able to hear the subtleties, you really have to live there for a while...