Good questions, Justin, and even self-described Austrians today would give different answers. So, for starters, check out my recent article on this stuff.
I think the best way for me to give a first response to your question (besides pointing you to that article) is to just list a bunch of statements that I think are correct (but some other Austrians might disagree):
==> Hayek thought he was elaborating on Mises’ critique of socialism. He didn’t think he was backtracking or conceding anything.
==> Lange and the other market socialists thought Hayek was conceding that Mises’ original claim was too strong. Rather than socialist calculation being impossible even in principle–as Mises had claimed–they took Hayek to be backing off and now saying it was only impossible in practice.
==> Austrians like Murray Rothbard and Joe Salerno think that there really was a huge difference between the Misesian “calculation problem” and the Hayekian “knowledge problem,” whereas Austrians like Israel Kirzner and Pete Boettke think they are two sides of the same coin.
==> A lot of people say things like “At first the economics profession said the Austrians lost the debate, but after the fall of the USSR, people realize Mises was right.” I guess I’m happy anytime someone admits he was wrong, but this actually doesn’t make sense to me. In my understanding of it, Mises wasn’t making a prediction about the viability of a socialist political regime. He was instead claiming that from Day One a truly socialist society would not be able to engage in economic calculation.