My mom has tabloids from the 50s. They had very similar scandals as now.
Were I to wake up after 60 years, I think I’d be most stunned by the evolution of language. Apparently the word “reality” has mophed to be a synonym for “game show of questionable worth.” Text is now a verb. As is dialogue.
ATMs/EFTPOS and Electronic Banking would also be a big shock, I imagine- going to a ATM machine, putting a plastic card in it, punching some numbers, and having it dispense money right there on the spot (Ditto EFTPOS, swiping your card at the counter of a retail store, entering numbers, and walking out the door with your stuff without actually having to hand over any money).
The fact that you can do this almost anywhere in the world- you could wander up to an ATM in Ulan Bator and withdraw money in the local currency from your own account- would be a cause of even further surprise.
Being able to call internationally for practically nothing, and instantly- just pick up the phone, dial a number, and you’re instantly talking to your friends, family, or colleages in Sydney, London, or Casablanca would also take some getting used to.
And Movies- imagine someone from the 1950s seeing Star Wars, The Matrix, or The Lord Of The Rings for the first time. (Probably best not show them 2001: A Space Odyssey, lest they wonder why they can’t take a holiday to the moon). Finally, the fact that PanAm went bankrupt would come as a complete shock, too, I imagine- weren’t they the biggest airline in the world in the 50s and 60s?
Also there’s no concept of “responsibility.” Yeah, I murdered my entire family, 14 strangers, and my neighbor’s dog, but it wasn’t my fault–I had a bad childhood and didn’t get into college.
Everything is society’s fault.
Well, Ray Bradbury touched on it in 1953 in Farenheit 451, though the 1966 film adaptation took the idea of interactive TV much further.
For that matter, the “telescreens” in 1984 could also send and receive.
This was what I came to post.
Also, they say That word on television!!
What, “Pregnant”? “Virgin”? “Gyrate” and/or “Hips”?
Why is everybody so thirsty all the time? Everybody’s carrying gigantic cups of coffee and bottles of soda. And why are people paying for water?
The Presidency has pretty much become a Bush/Clinton/Bush/maybe Clinton monarchy.
Everybody goes to college, and many get graduate degrees.
Single women live alone, not with mommy and daddy or a roommate.
And the corollary: standards at many of the largest colleges are much lower, since a college degree is now practically compulsory.
I so disagree. New Wave, like the sudden spread of overdriven vacuum-tube amps to every chump in the 60s and the spread of turntables to every street corner and club in the 80s, was a revolution of cheap, mass-market technology (in this case, cheap, portable synthesizers).
Impatience: the idea that just because you can get your burger and fries, or your dry cleaning, or your photos fast, that that means you have to.
Besides movies on demand, being able to watch your favorite show(s) whenever you’re ready, even if you were out of town when they were broadcast. Plus, the cult mentality that has built up around certain shows would be baffling.
Not being able to gauge someone’s age instantly by the clothes they wear. That guy’s 40, and he’s wearing jeans? And he’s not even a farmer or a dock worker? That girl is 10? Who let her get her ears pierced?
Similarly, people not dressing up as much as they used to. All those people at the airport – they look like they’re going to clean the garage! And when people do dress up, what on earth are all those hair products? And men and women getting their hair done at the same shop? What’s a salon, I thought that’s where you grow plants.
How hard it is to get away with anything – they have his DNA (what is that again?), his fingerprints, security video showing him entering the building, and the ballistics tests; he’s going down. Except, not, because there are also more laws and more legal red tape, and, as [bAnnie-Xmas** points out, greater reluctance to convict.
There are how many teams in MLB? Three divisions in a league? Auto racing is a sport? An “Oriental” guy playing basketball? Women playing basketball? The top golfer is named Tiger? What does “mixed-race” mean?
Sharing of information. Used to be, a person’s knowledge was dictated by how old they were, how extensive their education was, what experience they might have had in a particular field, and how much reading and studying they did on their own. For instance, I was told about this one family who heard the breaking news on 12/7/41, and had to ask the ultrastudious neighbor kid “Where’s Pearl Harbor?” Now anyone can hop onto Google or Wikipedia or SDMB 
and dial up any subject they want to know more about. They don’t have to have lived it or researched it extensively.
People in their sixties not looking it, by 1950s standards. In those days, if you were 60, you had one foot in the grave. Now you might see a 60 y/o out jogging (what, is he military?) and mistake him for 40. Meanwhile, the jeans-wearing 40 y/o I mentioned still gets carded at the liquor store.
When Armstrong got to the moon, was Alice already there?
Eh, I disagree. In the 1950s, rich people got a lot of press for doing nothing more than being rich. One side effect of the cultural revolution was reserving admiration for people who achieved something in sports or the arts. Then the bar gradually lowered on “achievement”, so we’ve merely come full circle.
I don’t know aobut falling asleep in the 50s or 60s - but if I had fallen asleep in the mid-late 1980s, and woke up today, I’d be shocked that Cyndi Lauper was a one-hit wonder, while Madonna was still around releasing hit singles.