It seems to me that Popper's solution does not address the more difficult problem of induction that Hume calls the Principle of Uniformity of Nature. In other words, we might find evidence against a scientific claim not because it was incorrect when it was formulated, but because Nature dramatically changed her rules sometime later or in a different region of the Universe. A hypothetical example proposed by Nelson Goodman, is that there is no way to tell the difference between green and grue, which is an imaginary color that looks green until some point in the distant future when it will look blue to the eye. Note that the existence of grue is trivially falsified by observation after the moment in the future when its appearance changes.
Presumably, Popper would suggest Occam's razor would reject the concept of grue. But that presupposes that the law of parsimony holds true, which isn't obvious. Popper suggests that, 'We prefer simpler theories to more complex ones "because their empirical content is greater; and because they are better testable"'. But that seems to me either a very practical reason untied to the actual truth of the law or simply begging the question.
Or perhaps he would say that Grue Theory isn't really falsifiable and therefore isn't a scientific theory until it can be falsified. But it's difficult to see how Grue Theory is different than, say, General Relativity which waited several years for the technology needed to produce definitive tests of the theory. In some ways, Grue Theory has the advantage in that it points to a specific moment when its claim can be definitively tested, unlike most scientific theories.
Did Karl Popper directly address the uniformitarian assumption?