Two posts by Tumblr users lohelim and kk-maker summed up the exact brilliance of Steve Roger's reawakening at the end of the film (links to original sources here and here):
The costume department deserves so many kudos for this, it’s unreal, especially given the fact that they pulled off Peggy pretty much flawlessly.
1) Her hair is completely wrong for the 40’s. No professional/working woman would have her hair loose like that. Since they’re trying to pass this off as a military hospital, Steve would know that she would at least have her hair carefully pulled back, if maybe not in the elaborate coiffures that would have been popular.
2) Her tie? Too wide, too long. That’s a man’s tie, not a woman’s. They did, however, get the knot correct as far as I can see - that looks like a Windsor.
3) That. Bra. There is so much clashing between that bra and what Steve would expect (remember, he worked with a bunch of women for a long time) that it has to be intentional. She’s wearing a foam cup, which would have been unheard of back then. It’s also an exceptionally old or ill-fitting bra - why else can you see the tops of the cups? No woman would have been caught dead with misbehaving lingerie like that back then, and the soft satin cups of 40’s lingerie made it nearly impossible anyway. Her breasts are also sitting at a much lower angle than would be acceptable in the 40’s. Look at [Captain America's] eyes. He knows by the time he gets to her hair that something is very, very wrong.
Nick Fury totally did this on purpose. There’s no knowing what kind of condition Steve’s in, or what kind of person he really is, after decades of nostalgia blur the reality and the long years in the ice (after a plane crash and a shitload of radiation) do their work. (Pre-crash Steve is in lots of files, I’m sure. Nick Fury does not trust files.) So Fury instructs his people to build a stage, and makes sure that the right people put up some of the wrong cues. Maybe the real Steve’s a dick, or just an above-average jock; maybe he had a knack for hanging out with real talent. Maybe he hit his head too hard on the landing and he’s not gonna be Captain anymore. On the flipside, if he really is smart, then putting him in a standard, modern hospital room and telling him the truth is going to have him clamming up and refusing to believe a goddamn thing he hears for a really long time. The real question here is, how long it does it take for the man, the myth, the legend to notice? What does he do about it? How long does he wait to get his bearings, confirm his suspicions, and gather information before attempting busting out? Turns out the answer’s about forty-five seconds.
Again, there's the reasons he stops running, and realizes he's in America, or something close to.
When alerting SHIELD to Roger's escape attempt, she calls out "Code 13" in English. This is Steve's first clue that something isn't quite right.
As he gets into the main hallway, Steve knocks down a black man. None of the Axis powers would have let a black man into their ranks so easily.
Just as he runs outside, Steve is nearly run over by a yellow car, which, while noticably different from 1940s era vehicles, is unmistakably a yellow cab.
Also, just where he looks, there's an American flag hanging.
On top of all of this, note where Steve stops. There's no mistaking it, it's Times Square. The new lights and signs drop it right into the uncanny valley, but the street layout and many of the buildings are still there. It's all of those that finally let him put the pieces together.
It's explicitly stated in the film that Steve realizes that he's being manipulated by the fact that the radio is playing a baseball game he'd already attended. It's also explicitly stated that they were trying to break the news to Steve gently by first making it seem like he's still in the 40s. They weren't trying to make him feel weird by deliberately making the facade crappy. That's WMG.
And the stuff about what makes Steve realize he's in America is based on the assumption that Steve first assumes that he's in another country, which isn't established. The fact that Steve recognizes that he's in New York City by the fact that he recognizes various sights is right on the surface.
Removed:
It's explicitly stated in the film that Steve realizes that he's being manipulated by the fact that the radio is playing a baseball game he'd already attended. It's also explicitly stated that they were trying to break the news to Steve gently by first making it seem like he's still in the 40s. They weren't trying to make him feel weird by deliberately making the facade crappy. That's WMG.
And the stuff about what makes Steve realize he's in America is based on the assumption that Steve first assumes that he's in another country, which isn't established. The fact that Steve recognizes that he's in New York City by the fact that he recognizes various sights is right on the surface.