assuming the following:
You agree with Popper's critique of Plato's politics.
I think Popper's understanding of Plato's politics is based upon a misreading of Plato's Republic. It is a common misreading, but a misreading nonetheless.
When asked directly (in the Republic) what is the ideal society, Socrates responds with a description of a simple agrarian society, not with the complex, controlling society that is developed in the Republic.
Socrates's interlocutor Glaucon is in some disbelief, and asks about luxury goods. Socrates repeats his assertion that he believes that a simple society with modest aims and production is best.
Upon further pressing, Socrates describes a society with an energetic pursuit of luxury goods as a society with a "fever". He immediately points out that to produce and protect these luxury goods or riches will require a number of things. It will inevitably result in war, which Socrates says is responsible for a great evil.
However, Glaucon seems unperturbed by this consequence of a society "with relish" as he puts it. So, Socrates follows Glaucon, and explains more of the consequences of a "feverish" society. Various solutions to problems are proposed. However, as the book proceeds, each solution to previous problems seems to lead to new problems. Ironically, although the original point of Glaucon's rejection of the simple society is based upon an appetite for luxury items, luxury items are denied to the populace as one of the solutions to one of the problems. The whole project of adding solutions to problems, which solutions create new problems, leads to the monstrosity that is described in the Republic.
According to my reading, the society which is elaborated in the Republic is a reductio ad absurdum, or a satire, and not a serious proposal for an ideal society.
Is there anything redeemable (or valuable to the contemporary person) about Plato's writings
Aside from the fact that Plato wrote on many other things than politics, I think there is something quite valuable in Plato's writings on politics. The warning which I read in Plato's republic is a good and valuable one. That is, instead of seeing our happiness in simple and modest society, we see it in ever greater material acquisitions. As a society, we see that there are problems, and we attempt to provide solutions to these problems. But we seem to be unaware that these solutions introduce new problems, and this approach to dealing with symptoms, rather than the root cause (material acquisitiveness), will not come to a nice end. It will not come to a nice end in two ways. One, it involves things that are not "nice", like wars and restrictive laws. Two, it will not come naturally to an end, but society will forever require further reforms. There is no end to it once we accept material acquisitiveness as a goal.