Let's get the obvious statement out of the way first: Christopher Nolan has completely altered the way we, as a culture, view Batman. Whether in the comic books, animated, or even (I'd wager) in prose, we all collectively picture a decidedly Christian Bale-esque Caped Crusader. We didn't used to do that. Nolan has made this iconic hero relatable in a way that's simply never been done before. Batman, of course, will always be a hero and he'll always be human (a few tangents in various comics not withstanding), but until Batman Begins, he was still just out of reach in terms of 'he could be anyone'.
Nolan's Batman could be anyone. The entire mythos of the trilogy is grounded in as much realism as you could possibly manage in a cinematic story about a man who dresses up as a giant bat.
Nolan actively resisted the more fantastical elements of Batman's history when crafting his trilogy. There was no chance of seeing Clayface, Killer Croc, or even Poison Ivy or the Penguin. The Batcave of the comics, with it's gigantic penny and life-sized Tyrannosaurus Rex, among a multitude of other museum grade artifacts was absent in favor of a much more utilitarian, spartan, and pragmatic setup. Even the weapons and vehicles - in all of their James Bondian glory - were toned down or revamped in order to preserve the overwhelming sense of actuality Nolan was going for. The point is made multiple times that everything Bruce Wayne uses as Batman is some form of military surplus. Even the Batmobile - that most sacred of Bat toys - went from being a retro-futuristic, avant-garde muscle car to an all-terrain assault vehicle. Last, but certainly not least, Nolan's Batman doesn't wear a costume to fight crime, he wears practical (albeit stylized), functional armor.
But how does all of this tie in to our collective intelligence as movie-goers, you ask?
It's not nearly as simple as I'm about to make it sound, but to be fair, I've had some time to turn all of this over in my mind, so here you go:
All of the realism that Nolan painstakingly created requires far LESS suspension of disbelief than you (as a Batman fan) were perfectly willing to put forth. This in turn frees up your mind to make guesses, to fill in a gap using the clues you've been given, to think for yourself and not have to be told.
Now, imagine for a moment that your only exposure to Batman is through Nolan's films. Sure, you've heard of various people that are connected somehow to Batman, but all you really know is what you've seen on the screen.
Batman Begins gave you the ground work and started teaching you how to think in the context of Nolan's Gotham. It was very paint by numbers. I don't mean that in a bad way, I'm simply saying that the film told you everything you needed to know as soon as you needed to know it. You know from the onset that this is an origin story, so it makes sense that you'll be introduced to everyone and everything in such a way that the events make sense. Things are explained either before they happen or directly after so there's no room for confusion. Nolan takes this route all the way to the final scene of the film, with Gordon letting Batman know about a new threat to Gotham in the form of the Joker.
The Dark Knight built on the education you had received. There were stretches of time where you were told nothing and allowed to see if you could figure things out. Then, just to make sure everyone was on the same page, you would get an explanation. If you had made the correct connections, you were rewarded with validation. If your ideas had led you somewhere else, you were shown back to the correct path. As with Batman Begins, but continuing the pace of Nolan's 'lesson plan', the final scene is Batman fleeing from the many police officers chasing him, and that's it. There's no indication of what will come next. You're simply left to wonder.
The Dark Knight Rises furthers that learning curve. The plot is given to you in such a way that you never stray too far from the important aspects, but the underlying facets of Batman are left, for the most part, for you to find on your own.
Selina Kyle is never referred to as Catwoman, but that's not an issue. You know that she's a thief, you know that she has reasons for why she does the things she does, and you know that she has a nebulously defined relationship with Batman that goes beyond Crime Fighter and Crime Committer. To you, Selina is the name of a person. She's more than a feline themed villainess. The leap you take is that - despite her not being given a comic book name like Catwoman - she has a rather important role to play. Not just in the main plot, but in her interactions with and influences over Bruce Wayne and Batman. Her presence determines a fair amount of our hero's decisions even though you aren't expressly told about all of them. Sure, the obvious ones are right there for everyone to see, but in terms of Bruce's/Batman's growth, there are various bits of depth and shading appearing that you really only see in hindsight.
Bane - being the main antagonist - has a slightly different set of rules. You get all of him. A fully formed picture is utterly necessary to appreciate the level of villain he's supposed to be. He, too, has no alter ego. He, too, is a person. He is simply Bane. It's an extremely subtle maneuver, but just like with Selina, Bane is made more real by using his own name. The changes he makes to Bruce/Batman are far less subtle than those Selina makes but they are no less important.
The story arc of John Blake is an exercise in multi-tasking. It has to introduce and keep you identifying and engaged with a character while providing you with a bridge between the two other major characters. Selina is - for the most part - subtle. She's controlled, contained, and reserved. Bane is about as subtle as a sledgehammer. Blake vacillates between both of them and acts as your anchor. His actions can sometimes be extreme and reckless, but other times they can be focused and plotted. At the end, when you find out that Blake's real name is Robin, the comic geeks in the audience groaned but you didn't. You know who Robin is and what his role is. Nolan tosses this tidbit out there for two reasons: 1) Acknowledgment for those of us that know the history, and 2) So all of us can look back on the movie as a whole and see that Blake was always right there fighting alongside Batman, helping him, setting and keeping things in motion that will make Batman's job easier.
Would I have preferred the lady in that scene to refer to him as 'Grayson'? Yes. I think it would've made the line less... hokey. But using my example of someone who only really knows the Nolan version of Batman, I understand why the line is what it is. More importantly, however, is that Blake - like Selina and Bane - never has to struggle under the weight of an alter ego. He's a human being. He has a history that's all his own, and he is driven to act the way he does for a myriad of personal reasons.
Miranda Tate is the character that really measures your ability to make intuitive leaps. She appears out of nowhere fully formed and the relationship between her and Bruce seems to move at a pace far too fast to warrant the amount of emotion between them when they eventually sleep together.
This is where Nolan puts his trust in you to pick up his clues. You know from the onset that eight years have passed since the end of The Dark Knight. Eight years is a long time in anyone's perception, but especially when we're asked to consider the world of corporate politics and the ways a company - even a whole city - can change. In her introductory scene, it's established that she's been around for a while. The way Bruce and Lucius Fox talk about her, it's casual and normal. They've been talking about her long before now, so it's not quite that abrupt when things get more personal. These characters have been interacting (on some level) for at least months and at most, years, that we simply weren't there to see.
The reveal of Miranda as Talia works very well within the context Nolan has spent three movies creating. The fact that Batman didn't see it coming is believable because he's known her for so long. He had no reason to think she was anyone other than who she said she was. And you - like Batman - didn't see it coming either, because by now, you know to trust Christopher Nolan. What he tells and shows you feeds directly into the next piece of information you're going to get.
Except when he doesn't want it to.
At the time of Miranda's betrayal, Nolan has spent two hours telling you about Bane's legend. Every single sign, marker, and hint point to exactly one location. And you fall for it, because why wouldn't you? You have no good reason not to.
It's Nolan's penultimate ruse. Had you wondered why he was being so very blatant, almost to the point of ham-fistedness - when you've been taught to think freely and resist being steered - you may have realized he was leading you down the wrong path on purpose.
But you were shocked and surprised, the same way Batman was. And that means Batman is fallible - just like you.
Of all the things that make Nolan's Batman relatable, it's who he surrounds himself with that really drives the point home. His enemies are just as human as he is. He can defeat them as long as he is smarter, faster, or stronger than they are. He also has people who trust him, count on him. And he has people he can turn to when he realizes he can't do something on his own. And this Batman DOES realize that. He figures out very early on that he needs help (and not just from Alfred). The Batman in the comic books has the luxury of time. He's already been around for well over 50 years and he'll continue to stay, but in Nolan's world, people age. Their scars heal, their traumas become more manageable, and their priorities change.
And that's also why he gives us credit for being smart. He knows we can appreciate the chance for our hero to not only have an ending, but a good ending. A human ending.
He knows that we can appreciate the over-arcing theme of the entire trilogy: Bruce Wayne is a person, but Batman is a symbol. And that's how it should be.