So, one of the things that I think being curiously unmentioned so far? Races. Now, in the real world, racism and stereotypes are a function of observer dissonance and culture more than anything genetic; in short, not a lot of innate differences. However! That is very much untrue in D&D. At the absolute very minimum, elves and dwarves have lifespans that make most races look like mayflies.
Here's a funny thing about technological development. Most of our modern advancement is the direct result of computers making it extremely easy to do research; prior to computers, a lot of money and time was devoted to either trying to painstakingly dig up previous research, or reproducing results when you didn't find anything. In terms of long lives? That wasted time and energy becomes far less, because you have people still around who can tell you about the results. Or at least remember something similar to point you towards. This gives elves and dwarves a huge, huge advantage when it comes to cultural and magical advancement. That's not something you see in D&D. In fact, such a thing is likely the reason for the level cap very early editions implimented!
D&D, in general, is a very human-centric game. Humans are everywhere, they're like flies, they form the majority fo cities, etc. But, when you get down to it, there's a lot going on that makes human advancement stand out. They don't really have a natural inclination towards development like gnomes, they don't have long lives and affinity for magic like elves, they don't have dwarven crafting skills. Humans seem to thrive in D&D because they're like rabbits - they breed everywhere, and they''d overpopulate in a heartbeat if there weren't so many natural predators (ie monsters) killing them off.
While we're on the matter of breeding... what's up with half-orcs and half-elves? The implicit assumption is humanity as the other half. Can we have half-human/half-halflings or half-dwarves? Are humans the only ones who can breed with other races? Here's an amusing conclusion that I jokingly came up with once - humans are actually the children of orcs and elves. That's why you get half-elves and half-orcs - they're already all "one race," at least in terms of having kids. Even if that's just a joke, you can bet your arse that more than a few people will come to that assumption and claim it as fact to look down on other races. Just a curious aside.
Anyways, back on subject. Different races are going to have vastly different magi-technological advances. When people talk about dwarven craftsmen being the best, we're going to be talking about a culture that has literally centuries of experience in their craftsmen. Individually. I don't think the impact can really be underestimated. And that's before we start bringing in aasimar, tieflings, dragonborn, aarkosha, genasi and the rest of Volo's / MM's races.
Funny thing about human psychology - we tend to gravitate towards those that share the same qualities with us. Just how difficult is it going to be for all these races to get along? Is that really the root of the good versus evil races - just the races that can get along together versus the ones that can't?
Classes
Now, D&D classes are basically your profession. One thing that's a curious lack is that there's no "production" classes. Farmer, blacksmith,
innkeeper, lumberjack, fisher, etc. Probably because they're not adventurer occupations. However, here's a curious question to consider - are these truly different classes, or are they following the same paradigm as adventurer classes? What does that mean? Is a farmer really its own class, or is it a subclass of, say, Druid? Remember, druids get spells that encourage crop production and to take care of animals. Certainly, learning druid magic would be the equivaelnt of advanced farming techniques.
How aware are people about classes? And levels? A single high level Fighter is worth more than an entire army... and I bet you the powers that be know it. Is this a world where might makes right? When you get right down to it, if you want to maintain power, you're going to need military might to do so. Nobles are going to be given advanced training over others so that they'll have a higher level, and thus be more likely to survive. Anyone proven to have advanced skill is likely going to be targetted by local governments - either for recruitment, or elimination as a threat. Advanced magical items will also likely be shared and used within noble families. The king's crown, thrown and rod are quite possibly artifacts in its own right that give him literal dominion. Do nobles train as bardic colleges for their social acumen, magic and lore? Or rogue? Imagine that as sub-classes - socialite and politician. The real social rogue! And lets not forget what I mentioned before, about long lived races - elves and dwarves, as long as we don't implement caps of some kind, are going to average higher levels than anyone else.
Honestly, so much of the world is going to depend on how classes work and how aware people are of them and levels. Spellcasters, at least, are aware of spell levels. What if there really are only fourteen classes (core plus psychic/mystic and artificer) and everything else is modified by your subclass and level? No matter how its implemented, however? What's going to remain is that high level individuals are going to be more important than almost anything else in the world as resources to manage. The'yre worth their wei... no, they're worth more than an army's weight in gold. Including equipment.
And then, what about crime? Paladins make it trivially easy to detect most contraband or other forms of smuggling. Imagine a city where all the guards swore an Oath of the Crown. Even at low levels (reachable by training), we have people with the ability to check all travelers using Detect Traps, Detect Lies or the like. Casual crime and gangs are very likely going to be down. On the other hand? Organized crime guilds are likely going to be not only thriving, but critical - you're going to need the support of Trickster clerics, arcane tricksters, warlocks and more to survive against the most basic of magical crime fighting.
Someone mentioned wizards versus clerics as a division of society. While I can't quite get that, I will bring up cleric versus druid. Both are "faith" classes, but with vastly different objects of worship - actual gods versus nature spirits. This could very well create a culture clash. In the real world, any time who religions met, most often, one was destroyed or absorbed into it. Chances are, based on human nature, clerics and druids are very likely to be at odds. Probably the same with the "friendly" rivalry of wizards, sorcerers and warlocks.
Alignment
Its a thing. Adventurer classes don't have the ability to detect it, but theer's enough of the occasional item that I'm sure it'll come up. Prepare for thought crimes!
gods
Objectively real. And they give stuff away.
Monsters
Probably the biggest consideration to a society. Now, D&D often resembles a pre-Industrial Revolution world for various reasons. City-state types with it being dangerous to travel between. Unlike the real world, however, the dangers of the road and forest are not to be underestimated. Monsters aren't animals or terratin. They're far more deadly. The world effectively lives in a constant seige state. You have to be prepared for monster attacks at any given time. This creates a situation where cities (due to magic) are very likely highly advanced, but unable to expand out as much as they would like. Occasionally, you get settlers, but how often will these new settlements get wiped out, even with the support of mercinary-like adventurers? I think RWBY, if anyone is familiar with it, is a great example of this kind of mindset. Without fortifications and natural defenses, its virtually impossible to set up new cities without a lot of help.
People talk about how adventurer classes are rare, but I have to question - if monsters are an ever present threat... why would it be rare? Military force is going to be a critical important thing fro any civilization, since they're constantly under threat.
Cosmology
Gods are real, and they talk to you. Angels can pop in a portal and come visit. Devils really are after your soul, but the path to get there far more complicated than just tempting you to "sin." Really, though, the most important detail?
We have a Star Trek situation. Planeswalkers who jaunt over to one world that's advanced, then go to one that's not. These worlds are all part of the same Great Wheel, and anyone advanced enough can come and go as they please. How's that for something mind blowing? How about when we have advanced societies (like an elven one with lots of high level warlocks and sorcerers) that can planeswalk at almost whim, visit distant gods, while the human society right outside the forest are still struggling to fend off goblins? Space age chilling next to bronze age.