@spendius,
Long story short, open society basically means democracy, as opposed to dictatorship. Popper is simply applying to political science his "science is faslifiable" idea. A society is open if it finetunes its political choices through trial and error, and therefore if its policy choices are reversible. You try an idea; if it works you keep it and expand on it; if it fails you try something else. That's what he thinks science should do, and also what societies should do. He calls that social engineering.
This approach is hampered when decision makers
outlaw or persecute those who disagree with them, because then these societies are unable to learn from their errors and are bound to keep making the same errors.
Well, I tried... In any case, this stuff is nowadays totally mainstream, at least officially. In practice, dissenters are being persecuted in the US and other democratic places too, and the capacity of democracies to learn from their mistakes should probably not be overstated. Technocracy, lobbies, the elites, many forces oppose change and the people's will, even in democracies.
Sometimes a dictatorship will actually change much faster. China comes to mind. It's been much more successful lately than India, which is democratic. Popper's warnings against one-man regimes do not apply to China. They have a certain way of maintaining the status quo while allowing for cautious change.
So you are right, there might be a third way. Although I remain suspicious of providential men, I sometimes find myself crying for one. Popper's weakness in philosophy of science was that he did not understand the value of intuition. Most analytical minds fail on that one. The same weakness translates in his political philosophy: he cannot see that sometimes, fiddling through your present system of democratic governance will just not work. Sometimes you need bold leadership, a revolution, a leap of faith... even if it's risky.