One of my favorite effects scenes from an old movie is the opening of Rouben Mamoulian’s version of Dr. Jekyll and Mister Hyde, the one with Fredric March. as I’ve said on this Board, many times, it starts with a POV shot of Jekyll playing the organ. His butler calls to him, and the camera swivels over to look at him. from Jekyll’s POV we see him get up, walk to the door and through it. As he passes the mirror in the hallway he looks directly into it and sees himself. The butler puts his coat on him, and Jekyll turns to go down the hall. The butler is already there, and opens the door, and jekyll goes out to the street and his cab. This is all done in one unbroken shot.
It must have been well-rehearsed, because it’s really complex, and a lot of things had to go right for it to work. They built a complete mirror-image room on the other side of the “mirror”. The guy playing the butler had to run around really fast to get from “mirrorland” to open the door (or else they had two identical-looking guys, identically dressed).
The scene was so impressive that people copied elements of it in later years. In one of the “Director’s Cut” scenes for Terminator 2 they had a similar mirror scene where they’re taking the memory chip out of Arnold’s head. After setting up the scene with a REAL mirror (framed in Post-It Notes), moving it to let you see it’s a mirror, they cut to a new shot where the “mirror” is an opening to a mirror set. In “Mirrorland” is the real Arnold and Linda Hamilton. In the “real world” is the model of Arnold’s head, with the hole and chip, and Linda Hamilton’s sister, playing the “real” Sarah Connor.
They duplicated the “actor changes around” bit of the butler in the first Superman movie (directed by Richard Donner, starring Christopher Reeve). When Superman flies off, after his first date with Lois, it’s clearly Reeve in his Superman suit, on wires. In an unbroken shot the camera tracks around to look at Margot Kidder as Lois. There’s knock at her apartment door, and she answers it, letting Clark Kent in. It’s, again,. clearly Christopher Reeve, dressed as Kent, his Superman suit nowhere in evidence. They had to move really fast to do all this smoothly. Ther are no “jumps” to indicate cutting of the scene, and this was too early for CGI “smoothing” of such jumps.
An echo of the OP’s John Garfield with the violin is The Sting, where you see Paul Newman’s character, Henry Gondorff, doing card tricks. The camera watches the moves, and, at the end, when you’re convinced that they just filmed a card expert doping these tricks, the camera tracks up to show Paul Newman’s face. Movie sites, like imdb, say that they cut away, and they DID use a card expert. But watch the shot carefully – it’s clearly an unbroken shot. That really is Paul Newman doing those moves.
Nowadays you can easily blend different scenes together to give the illusion of an unbroken shot – they did it during the “house collapse” chase scene in Sprecte, but they had CGI to help with that.