Horse vs. hoarse, morning vs. mourning
Right now you're most likely thinking "horse and hoarse? They're the same!" For most people in the English-speaking world they are the same, but a long time ago they were originally different, and they still are for a quickly-shrinking number of Americans in the eastern US. It's probably not important but it's still a legit dialect feature so I'm throwing it out here.
There are of course two sets here. Set 1 (/ɔhr/) is made up of most words where the spelling is simply or (fork, horse, morning, north, York) and all words spelled with war or quar (quarry, quarter, war, warm, warn). Set 2 (/ohr/) has all the words with alternate spellings oar (board, coarse, hoarse), oor (door, floor), ore (bore, core, more), and our (course, mourn, pour). For some reason, set 2 also includes several words with or spelling. Usually this means words with a p before the or as in pork, port, Portugal, sport but it also applies to afford, force, and ford.
So who keeps the two sets separate? There are two regions: ENE and the South. In the South, most people have both sets merged but there still are older people here and there who show a distinction. Dallas, New Orleans, and St. Louis have some concentrations of speakers with the distinction. Meanwhile up in ENE the distinction is going away in Maine and New Hampshire; but it's still hanging by a thread in Boston and Providence where people usually pronounce them similar or the same, and there isn't much relation to age. One person you may know with a bit of a distinction is John Kerry (Boston). The older Kennedys probably have it too but I haven't checked. Jay Leno (Andover, MA) seems to have the distinction, sometimes. Then on the Southern side there's Jimmy Carter.
And of course, you probably want to know what the two sets sound like. In the original pronunciation, still found in the older Southerners, /ohr/ (the hoarse set) sounds the same as with most merged speakers. /ɔhr/ (horse) is between /ohr/ and /ahr/ (barn, card) and sounds something like the raised /ahr/ of NYC.
The people of St. Louis used to have a unique system in which /ɔhr/ merged with /ahr/ instead of /ohr/ so cord sounded like card and horse came out as "harse." This has also been found in rural Texas and Utah areas. These days only older people in St. Louis have this feature and most people there have the same /ɔhr/-/ohr/ merger as everyone else.
And it seems there are sound files out there of people with the distinction. At the International Dialects of English Archive they have recordings of some old Southerners and New Englanders. Listen to the two Massachussetts samples, and North Carolina samples 9 & 11, and you will hear how /ohr/ and /ɔhr/ are pronounced different.
Whale vs. wail, which vs. witch
This is something else you may know about. Like the last feature, this one is what we call a "relic," because it's a receding holdover from the past which most North Americans don't have. For people with this distinction, words beginning in wh were pronounced with an "h" sound before the w. In fact, in Old English (before 1066) such words were spelled hw but in Middle English the spelling became what it is now.
One hundred years ago, the /w/-/hw/ distinction was fairly general in North America, and the only merged areas were big cities on the east coast like New York. Now, the merger is general, and the distinction is only preserved by older people in Canada and in the rural South.
Huge without the h
This is another "big northeast cities" thing like the Mary/marry/merry thing. It also didn't get mentioned in the Atlas. Words like huge and human lose their h so they come out sounding like "yuge" and "yuman." As far as I know it's in Philadelphia, New York City, and Boston.
Bright vs. dark L's
One fact that hardly anyone is aware of is that there are two ways to say the letter L. You can touch the roof of your mouth with the tip of your tongue, or not. If your tongue touches the roof of your mouth then it's a bright L. If the tongue doesn't touch then you have a dark L, or "vocalized" L as the linguists would say. Many people with certain accents will darken more L's than others. The Atlas people didn't study this variable because their survey was done entirely by telephone, and this is hard to notice over the phone. However, other recent research has shown that the leading area for dark-L's is Pennsylvania, not just in the Western PA (Pittsburgh) region but also in Philadelphia as well.
Also, people who have a complete /o/-/oh/ merger will usually say a dark L in words ending in -all (mall, small, tall) when the next syllable starts with a consonant, because bright L's usually pull vowels back a bit.