<...Popper, whom I respect, criticizes evolution as possibly non-scientific, in that it's predictions are not falsifiable.

You can't do an experiment to reproduce continental drift either, or thousands of other observed phenomena. That doesn't make the science false.

My personal take on it: evolution is a fact. However, like we discovered with the human genome, there will be a few surprises in the future when the mechanisms of genetic evolution are uncovered further.

My long-shot (VERY long-shot) guess: some undiscovered feedback mechanism other than natural selection where the environment, or viruses, or organism behavior, or something, somehow directly affects the offspring of the organism and its future genetic structure (Lamark, come home! All is forgiven!).

Whereas there is no evidence for this right now, such a capability would be so mind-bogglingly useful that if there were any way to do it, nature would find it. Closest analog I can think of offhand: the temperature at which alligator eggs are incubated directly affects the sex of the offspring.

Our own human ability to change our behavior in a geological instant in response to the environment (cultural evolution) works like this, in a Lamarkian manner. It is the human species' greatest asset.