The English version of LScD came out in 1959. It wasn't a straight translation; Popper worked on it. In my (somewhat vague) understanding he changed some stuff or at least added some footnotes (and appendices?).

Anyway Popper published plenty of stuff after 1946 including material from the LScD postscript that got split into several books, and also various books where he had the chance to say whatever he wanted. If he thought there was anything important to update he would have. And for example probability gets a lot of discussion in Popper's replies to his critics, and Bayes' theorem in particular comes up some; that's from 1974.

So for example on page 1185 of the Schilpp volume 2, Popper says he never doubted Bayes' theorem but that "it is not generally applicable to hypotheses which form an infinite set".