Almost every critic of the Austrian school, who is actually educated in economics has brought up the Austrians view of the firm, and the lack of a proven theory.
So, what is the view of the firm, and is there a sound theory out there?
I'm not sure, but if by "theory of the firm" you mean all of the neoclassical theories about oligopolies, cartels, etc. then I think one of the reasons Austrians do not talk too much about this is because this is not a natural market process, but a result of corporatism. The only Austrian articles and extracts from books that i've read relating to monopolies explain how they come about as a result of government sanctioned licensing, and the likes. Then again, I haven't read even 5% of what I was meaning to read so far, so I could easily be wrong here.
Oh and I forgot to mention. Von Neumann and Oskar Morgenstern (the latter an Austrian) came up with Game Theory.
As I understand Austrian Economics there is not the distinction between Macro and Micro economics that I was brought up on. All economics netts down to individuals carrying out specific actions, using the best information they have at the time, and making the best judgement calls that their experience and intelligence allows. The Firm is only a collection of individuals carrying out Human Action. There is no equivalent to the Marginal Cost = Average Cost nonsense that I was taught.