I've thought about Heisenbergs uncertainty principle with this, and I don't think it would be a show stopper.
That principle, in simple terms, means the more accurately you can measure the position of a particle, the less accurately you can measure the speed and vice versa. So for this machine to work all you need is to be able to measure the position but in an instant.
It applies at the sub-atomic level for measuring particles like electrons and muons. But, if you could identify the atoms and the position of those atoms, would the state of the sub-atomic elements matter?
I really don't know what resolution you need for a good enough copy. The storage and bandwidth would have to be enormous.
In 100 years time I am sure we would fit on a Class 100 MicroSD card :)