To a non-physicist, the gist of the Heisenberg uncertainty principle, or the observer effect phenomenon associated with it, is that studying an object changes the object. You want to know the position and movement of a subatomic particle, say, but to find that out you have to study it with energy, like a light beam, which allows you to identify the position by seeing how the collision with your measurement beam occurs. But that alters the target particle's movement so you can't know both.
Similar kinds of issues apply to modern-day epidemiology. We referred to this yesterday in a comment about the effect of maternal drinking during pregnancy affecting the future of their offspring. A Heisenberg analogy for epidemiological studies goes like this: if by studying something that has many contributing risk factors, the persons being studied change their behaviors, and thus their exposures because they know the results of the study, you can no longer estimate what the exposure risks will be.
Often, the change in behavior is of a magnitude that it's a major effect relative to the signal that's being studied. If you stop eating pork because a study says that eating pork gives you a somewhat increased risk of warts (it doesn't--this is just a made-up example!), then the effects of pork-eating will be changed by virtue of the exposure change and the knowledge that this is being studied. If this happens often enough--as it does with our 24/7 many-channel news reports--then tracking risks or measuring them becomes very problematic, except for the really major risk factors (like smoking and lung cancer) which are robust to small changes. The science and the scientist become part of the phenomenon, not the external observer that they need to be to do the science. This leads to many of the serious challenges to modern epidemiology, behavior, education, political, economic, etc. studies, including those of genetic causation. And since trivial risk factors are mis-reported in the news as big ones, the signal-noise ratio is even less favorable to clear-cut conclusions.
There is a kind of Heisenberg analog in evolutionary terms, too. If relative fitness--reproductive chances--are affected by both genome and ecologic contexts, and the differences are small, then what happens tomorrow to a given genetic variant, is highly dependent on all sorts of environmental or other genotype changes. A given variant won't have the same relative effect tomorrow as it did today, and since evolutionary models are about relative fitness, the evolutionary landscape changes.
This becomes Heisenberg-like not because it's about observer-interference effects in this case, but because the context changes can be as great or much greater than the net fitness advantage of a genetic variant. This means fate-prediction is difficult, and in this case the observer analog has to do with the screening-efficacy of natural selection. Changes in the frequency of an allele can change its net fitness effect. When fitness (like electron positions?) is not just contextual but essentially probabilistic, something that affects position (current relative fitness) affects evolutionary trajectory. That's one reason evolution is essentially unpredictable, except under unusually strong conditions, and in that sense not deterministic as it is viewed in the usual Darwinian concept, especially as put forward by those not versed in evolutionary theory--and that includes many biologists and all the blathersphere that invoke Darwin or natural selection in making pronouncements about society.