The topic is getting some play in the blogosphere due in part to the post on this matter by Sean Carroll (the physicist at Cal Tech, not the eve-devo biologist) on the Edge question of the year (see here and find his contribution on page 202-3). At any rate, there has been some interesting discussion from people in other areas that you might be interested in looking at (here, here, and here). The discussions give subtle takes on Popper's falsificationist dicta, all recognizing that the (at least common) understanding of Popper is way off. Pigliucci notes the problems that the Duhem-Quine thesis raise, i.e. the observation that theories are never tested directly but always rely on many auxiliary assumptions that can serve to insulate a thesis from direct empirical refutation. The discussion is interesting and may serve to temper simple minded resort to the falsificationist gambit.
One thing, however, that seems not to have been mentioned is that quite often we can find evidence for claims that are not falsifiable: for example, the germ theory of disease postulated germs as agents of disease transmission. It's not clear that existential statements are falsifiable, viz. the absence of attested black swans does not imply that black swans don't exist. We make many such existential claims and then go out and look for instances, e.g. germs, black holes, Higg's particles, locality conditions, etc. In other words, we often actively look for confirmatory evidence for our claims rather than looking to refute them. In fact, I might go further, in the early exploratory phase, finding evidence for one's views is actually more important that finding evidence that could refute them. Good ideas start out life as very fragile. There is always tons of apparent evidence that "refutes" them. Indeed, the more daring the proposal, the more likely it appears to be false (and perhaps the more likely that it is false). So, what does one do? Look for places where it works! And this is a smart thing to do. It is always fair to ask someone why their proposal matters. One way that it can matter is that it does something interesting, i.e. solves a puzzle, explains recalcitrant data, predicts a new kind of object etc. Evidence in favor of a proposal is what allows one to make demands on a rational listener. So, falsification as a strategy is useful, but only after a proposal has gained admittance as a live possibility and admission to this august group is paid for in verifications.
At any rate, the discussion is pretty good and there are links to other matters that might matter. It's always nice to see how others flounder with these large methodological concerns. Enjoy.