Oh what the heck, here are two of the problems that Robert May spoke of in the above quote:

The first problem concerned the time available for evolutionary processes to operate. Fifty years were to elapse before the first glimmers of awareness of weak and strong nuclear forces were to appear. Of the four fundamental forces recognized by today’s physics, only gravitational and electromagnetic (“chemical”) forces were known in Darwin’s day. But if the sun’s energy source was gravitational, it could not have been burning for more than about 20 million years. And chemical fuels would give an even shorter life. A different calculation showed that it could not have taken more than roughly 20–40 million years for the earth to cool from molten rock to its present temperature. These two calculations meant that either the earth was at most a few tens of millions of years old, or that Victorian physics was fundamentally deficient...Of course, the subsequent discovery of nuclear forces showed Victorian physics was indeed inadequate: the sun burns nuclear fuel; and the heat generated by the decay of radioactive elements inside the earth invalidates simplistic calculations about cooling rates. We now understand that evolutionary processes on earth have all the time they need.

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The second problem stemmed from the conventional wisdom of the day, namely that inheritance worked by a blending of maternal and paternal characters. The essentials of this issue can be grasped by considering a trait (such as height or weight) that can be described by a single variable.... It is [...] straightforward to show that, with blending inheritance, the variance of this trait in the next generation is halved. But persisting variability is the raw stuff upon which natural selection works to produce descent with modification; it was critical to Darwin’s ideas.... The resolution of this major difficulty lies, of course, in the fact that genes are inherited in particulate Mendelian fashion, not by “blending”. And, as shown in 1908 independently by Hardy and by Weinberg, under Mendelian inheritance variability remains unchanged from generation to generation, unless perturbed by factors such as selection, mutation, statistical drift, or nonrandom mating.