I see this thread is diversifying quite widely - maybe somebody should split it up into its various streams (or maybe it will resolve itself through a quantum Darwinian process into the most energy-efficient state if we leave it long enough...)
I found the Thompson paper quite exciting, more as an introduction to Zurek than anything. I'm the first to admit I lack the background in physics to get anything like a full understanding, still less be able to evaluate it wrt other approaches, but to me the quantum Darwinism concept begins to make more sense of QM for me: I have the feeling that if it became the mainstream view and I kept reading about it, I'd slowly get a handle on it.
I'm less convinced of the wisdom of slotting it into an idea of "Universal Darwinism" - especially at a time when adaptation is being significantly downgraded in the ToE itself and Darwinian social science explanations are increasingly found wanting. It seems Zurek himself is treating his approach as merely analogical to Darwinism, in a restricted sense: there could be other paradigms by which to explain it, perhaps.
But the idea of a continuum in the "internal" workings of the quantum state, which "collapses" in a particular way as a function of translation into the existing state of the environment presses all kinds of buttons about how the world is. The link to information as a foundational component of reality rears its head again.
One of the most interesting parallels with biological evolution is QD's dependance (if we ignore Campbell's assumptions about the Darwinian evolution of the entire universe from simplicity) on complexity. I'm intrigued by the rather bold assertion (if I understand aright) that there are complex and entirely unknown mechanisms at the quantum scale, just as evolution, though it seems a simple idea, depends on the inordinate complexity of the mechanisms in the cell, as we have only recently come to appreciate.
I've come to think that life is irreducibly and inherently complex (I'm not talking about Behe, more Denis Noble or Sy Garte!), and the thought that it may be equally so at the "basic" quantum level is rather mindblowing. It makes the idea of a reductive mechanical view of reality less tenable - which in turn potentially opens up all kinds of "supernatural" phenomena to scientific assessment (just as "occult" gravity became available to science through Newton).
At the same time, "quantum Darwinism" seems to me to point in a greayter way to the need to see God as the unifying and originating cause of it all - and to make his ongoing interaction with reality far more plausible than in "the mechanical philosophy" of metaphysical naturalism.
Such were the immediate effects of the paper on my imagination - probably more than on my reasoning, given my lack of background. But thanks a lot for the stimulating link. As so often, physicists seem to think more like theologians than do many biologists.