In two comments, our friend Nikolaj has provided textual evidence that appears to support the view that Mises was in favor of a 100% reserve banking system, presumably along the lines of that supported by Rothbard. At the very least, these passages are said to suggest that Mises rejected free banking.
First, if Nikolaj is correct, then Mises must indeed have been VERY confused. How he could take those positions in 1949 and 1951 then turn around at another point in 1951 and then in 1952 (where my two quotes came from) and say apparently the exact opposite is, suffice it to say, very strange. Surely a man as brilliant as Mises (that is not sarcasm) could have seen these obvious contradictions. So what gives?
I think the answer is that all of these passages in which Mises calls for "100% reserves" are ones in which he is proposing schemes of monetary reform given the existence of government-monopoly central banks or other regulations on private money production. He is not proposing 100% gold reserves a la Rothbard as the ideal system. Rather he is trying to find a way to limit credit expansion in a world in which central banks already exist. That is a very different question from the usual fractional reserve free banking vs. 100% gold reserves debate.
The quote from the 1924 edition of TTOMAC that invokes Peel's Act and the suppression of further issue of fiduciary media takes place in Mises's discussion of then-current policy proposals (e.g. Fisher and others). Given the weakening of the gold standard and the intervention of central banks, imposing a Peel's Act type restriction on the creation of deposits and notes is not a ridiculous idea. Of course Peel's Act historically was imposed upon the Bank of England simultaneously with granting it a monopoly of note issue in London and other monopoly privileges. If you have a central bank with a note issue monopoly, subjecting it to statutory limitations might make sense. Mises just wanted to transfer this idea to 20th century systems and apply it to deposits consistently. But this is a second-best proposal. So using this passage to support the idea that Mises was in favor of a Rothbard-style system as the first-best monetary arrangement is not nearly as clear as Nikolaj would have it.
I would make a very similar argument about the 1951 quote from The Return of Sound Money. In fact, I think my argument is even stronger there. Earlier in that essay, which was tacked onto the 1954 edition of TTOMAC, Mises wrote:
The quote from Nikolaj comes later in the essay, but he neglects the context. Note that his quote starts with "The first step must be..." First step toward what? Well the context of that quote is how to return to a gold standard GIVEN the then-current US monetary institutions, including the Fed and various other forms of government intervention, not to mention the proclivity toward deficit spending, which Mises wishes to combat.
That this is the context is clear three paragraphs later when Mises writes:
Just to pile on a bit, he later says:
Finally, you're going to have to deal with what Mises has to say on p. 443 of Human Action, emphasis mine.
Free banking is the only method available for the prevention of the dangers inherent in credit expansion. It would, it is true, not hinder a slow credit expansion, kept within very narrow limits, on the part of cautious banks which provide the public with all information required about their financial status. But under free banking it would have been impossible for credit expansion with all its inevitable consequences to have developed into a regular - one is tempted to say normal - feature of the economic system. Only free banking would have rendered the market economy secure against crises and depression.
Finally, there is the famous quote of Cernuschi where he says he wants free competition in banknotes so that "nobody should take banknotes any longer." It's worth pointing out that this is only about banknotes; it says nothing about deposits. And it says nothing about fractional reserves! If Cernuschi had said "I want to give everybody the right to create fractional reserve liabilities so that nobody should accept fractional reserve liabilities any longer" then that would be evidence, if Mises approved of the quote, for Mises objecting to fractional reserves/fiduciary media per se. But that's not what Cernuschi said, and we've already seen Mises's concerns about banknotes above. That concern is, however, not a concern about fiduciary media per se.
So Nikolaj's passages don't persuade me and there remains significant evidence that Mises was both adopting a monetary equilibrium approach to inflation and that he did not object to the creation of fiduciary media in a world where government central banks and other interventions were absent and competition among banks, who were subject to the same rules as all other business, was present.
[ADDENDUM: To be clear, I am not arguing that Mises was clearly and unambiguously a MET-fractional reserve free banker. The evidence is not that clear. What I am arguing is threefold: 1) the preponderance of the evidence is that Mises was more or less a MET-FR-FB; 2) there is very little evidence at all that Mises thought a Rothbard-style 100% reserve system was the first-best ideal monetary system; and 3) where Mises does recommend 100% reserves, it is almost always in the context of a program for monetary reform given that government is deeply entwined in the banking system.]