Weeellll even in the comics he still isn't quite 'all there' in terms of being 'hip' to the 'modern world'. I mean sure he'll use a bluetooth headset and we saw him using a tablet, but he's a super soldier. He's got a photographic memory, he's also got a boost in learning tactics. So really... it wouldn't take him much time to get 'used' to the 21st Century, so he reads his briefings on a tablet instead of a notebook, he makes a call on a cellphone linked to a bluetooth. Similar actions, just new toys. Plus he's not an elderly man who lived through WW2. I think too many writers go "oh I'll base him on my grandpa would treat technology." And while, sure given that he didn't grow up with the stuff we did, it's all pretty alien - but he's still a young man, he still has a sharp mind. He'll figure it out. I'm glad they didn't have him fumbling around a cellphone calling it some "dad busted doohicky" and being completely lost around computers. While he's surely not up to the level of a teenager around a computer, I'm sure he's been able to figure things out. "Oh so if I click this icon I can do a search. Gotcha."
I think the biggest challenge will be the "pop" cultural references and other more recent developments. I mean even someone saying "Let's Rock and Roll!" won't quite have the same feeling for him as "Let's kick some ass!". Or even people referencing like Nixon or Clinton or Bush will be given a "huh... ohhh okay..."
I'd love to see Captain America 2 open up with him maybe researching the past 70 years - him sitting in front of a laptop with Wikipedia up or going through files - could even make a neat opening sequence. Show him seeing V-J day video/pictures, going through to Korea, Elvis Presley and the birth of Rock n Roll, the whole Post War USA, Rolling stones, the Beatles, the hippies, Vietnam War, Nixon/Watergate, Star Trek (since they really can't use Star Wars lol), Video Games, Reagan, Desert Storm, Lewinsky and Clinton, Cole Bombing, 9/11, War on Terror, Reality TV... lol
Then, have him get some call from Nick Fury about "We found something..." and then we could have a scene aboard the helicarrier and setting up the reveal of Bucky... but show the Red Skull returning (or Arnim Zola... or Baron Zemo) and Hydra. But I woudl like to see the "man out of time" angle sort of replaced by more action. Sure have a few minor jokes at his expense, but by this point he's more 'in touch', maybe not entirely there yet, but he's getting there. Or slightly messes up a reference.
Love to see Stan Lee do his cameo as like a comic book writer from the War, that tells Steve that 'hey I used to write your comic book... and also these guys... " pulls out an old comic book with what looks like Winter Soldier. "War department had us dramatize your adventures, and those of other heroes during the war. Lesser known guys. While you were fighting Hydra, these guys were doing this. I wrote 'em until the 50s, damn that Wertham. This was one of the last few I did." and then you see like "The Adventures of The Patriot" against... "the Winter Solider."
Sort of taking a page from that comic series "The Twelve" of 12 "super heroes" from World War 2 that were found in suspended animation in the 21st Century. The other "lesser known" heroes.