Until I took a Universal Studios tour 37 years ago, I never knew about the technique of rear projection used in most movies. Nowadays, I see it in every Hollywood movie I watch.
One of the 'tricks' of rear projection is to ensure the 'point of view' is the same for both the projected image and the subject. For instance, if the projected image is shot from curbside looking down the street (let's say the left curb), and the camera is situated to the subjects' left side (your right), everything would seem 'backwards'. In this case, the camera must also be from the 'left curb', or subjects' right side, when facing you.
The same would be true of shadows and sun position.
Or, use a 'generic' image that is shot 'down the middle' and shoot from straight on at the subject or very slightly left or right of center. Think about the image on the wall behind Dave Letterman and the camera position relative to the image and to Dave.
If I were to attempt such a shot, I'd most likely use a projector screen. I just happen to have one from my slide projecting days. Having a computer projector attached to a computer is the preferred method these days. Then have a king-size flat sheet either tacked to the wall so it's very flat, or, use a cheaply built from 2"x3" frame to attach the sheet to, especially if projecting the image from behind the screen.
Perhaps the biggest issue I can envision is shadows from the subject upon the background image. If some outdoor 'mountain view' is used, for example, there wouldn't be any apparent shadows if it was shot with a real mountain as a backdrop, as the shadows would be on the ground that would be below the image the camera sees.