This is what I first thought of in regard to trek, a true flat thin screen monitor!
Well, now flying cars, but at least THAT wish came true, right? 
Interocitor!
Not only flat, but triangular. How could you all forget This Island Earth?
ETA: WiFi teleconferencing too
Although he used regular tubes something I always appreciated about Cameron’s ***Aliens ***is how he was smart enough to mask off all the CRTs screens into 16:9 format. Went a long way to keeping them from being too dated. Though there are those huge clunky camera lenses on the helmets (GoPros they ain’t!) However just the fact that GoPro Cameras are now appearing on real soldiers helmets gives him major props for seeing the logic to it.
Here’s a real weird one: In the (rather good) 1950s scifi-horror classic ***The Fly ***when told that his brother has a big invention announcement for him Vincent Price says to his sister in law, “What is it, flat-screen?”
I was watching Lost In Space episode “THE SPACE TRADER” #24. The Space Trader is seen using a flat monitor as he controls the weather.
As I’ve said elsewhere, we don’t know on what their technology was based. Maybe the duotronics of the 23rd century required the use of such a screen in the tricorder. Also, there is nothing to indicate that screen was anything like the CRTs of our day, other than its general configuration.
I always thought too that the viewscreens in the briefing room (which were obviously flatscreen) were just mounted so that everyone around the table could see them simultaneously. (About the big, bulky ones in Kirk and Spock’s quarters, I don’t know.)
Well the Discovery One was an American ship; the Leonov was a Soviet ship.
Nope, the big monster CRT monitors were also in the AI research facilities of the Americans.
The Jetsons had large, flat screen TV’s for home viewing.
A Doctor Who story The Ambassadors of Death (1970) has a scene where a flat screen rises out of a desk, shows a video transmission, then descends back into the desk.
It’s obviously done with CSO, because as the screen descends, the image disappears from the top.
To the screens on the back of the shuttle seats in the opening scene (after the Man-ape scenes) on the way to the space station.
There was a movie in which an astronomer in California constructed a device for listening to radio signals from space. The movie was a bit convoluted and involved the Soviets and possibly fake radio signals and biblical quotes from Mars.
Anyway, the astronomer’s family home had a flat screen video device mounted above the fireplace (in approximately 16:9 format. Wider than high, anyway.) They watched news shows and other things on the device so it was meant for consuming content.
Don 't remember the name or date of the movie, or the stars.
Bob
I remember George reading his newspaper on the screen, too. It seems the Jetsons predicted the death of printed papers.
Missed the edit window Red Planet Mars 1952
Not a bad movie except for the bible stuff.
The irony being that flat screens weren’t actually in widespread use in 2001 (although if anyone was going to use them it would be a space mission) but were by 2010.
In the film ** Rollerball ** (1975), James Caan is shown watching a large flat screen television attached to the wall of his room.
Slightly off-topic, but the BBC adaptation of Hitchhikers Guide had characters using what we all recognise now as basically a smartphone, with the display on the screen in shot. You don’t even recognise it as an effect now, it’s so common, and these days the display would probably be added digitally in post, but in those days the effects had to be done by a team of guys clambering about on the floor out of shot, with a rig that allowed the laboriously hand-animated computer effects to be projected up into the prop the actor was holding. And the quality of the animation was so good that most people assumed that it had been computer-generated, even though that was so barely achievable by the standards of the day that it would have been prohibitively costly even for Hollywood.
So good an example that Samsung brought it up during their spat with Apple.
The pad like device stuck in my mind as it was being used so casually, astronauts chew down lunch, check the news, just like any office 
Kirk signed off documents from his yeoman on a small pad like device, as long as the camera wasn’t pointed at it the wrong way, you wouldn’t spot that it was one of those pads for kids that work on pressure sticking a plastic sheet to a harder backing piece.
I just happen to have watched that movie a few weeks ago. I don’t really think those were meant to be flat screen. Here’s a clip of them (ignore the trippy music). They were made ‘futuristic’ looking by having them consist of four screens, one large and three smaller ones, all with different POVs (the film called it ‘Multi-Vision’). However the screens look exactly like regular tube TVs, just bigger. They are 4:3 and have curved edges and very rounded corners. Rather ironic considering they had to have been rear-projection and film (not video) based props (they’re a real, on-set practical effect, not an optical, process shot). They also are clearly meant to look massive and built into the wall, not a thin screen hanging on it.