(in response to my experience of working on a Mir shutter)
The shutter-speed dial is on a shaft that rotates with the movement of the shutter curtains, so it spins when you cock the shutter and then spins back in the other direction at release (you can see this from the outside). In the cocked state, the shaft is aligned so that the speed dial will point to the right value on the surrounding ring (which doesn't move with the shaft). So if you set the speed to read to, say, 1/50 in the *uncocked* state, the actual orientation is basically some random position.
It's been years since I was doing this, but as far as I remember, the only thing that the speed setting changes is the angle of a little cam on the shaft. The release is a two-step process: when you press the button it fires the first curtain, and when that little cam comes around to a certain point in the rotation of the speed shaft, it trips a release for the second curtain. The shorter the rotation to bring the cam into contact with the release, the faster the shutter speed. There's an explanation at http://rick_oleson.tripod.com/index-131.html, which indicates that the Leica II used the same basic mechanism.
As far as I could tell, you couldn't actually damage anything by misaligning the speeds this way on a Mir (or a FED-2, which also doesn't have any slow speeds); you'll just get the dial in the wrong position and shutter speeds that have nothing obvious to do with the reading on the dial, and setting the speed while the shutter is cocked should fix that misalignment. I didn't understand every bit of the workings, though, and I certainly didn't make any exhaustive search for ways to break the mechanism---but I *think* actual mechanical damage is not readily available.
By all accounts the models with the slow-speed escapement are another kettle of fish and you *can* break them by setting the shutter at the wrong time, but I don't know what the failure mode is.