Since none of the are integral to Austrian economic theory but a few of them are against opinions of Mises and Rothbard (and I wouldn't even disagree with the author's view points here), it's comparable to saying "Darwin said you should always explore distant nature in a naval vessel and he believed in God, therefore his theories are wrong".
To substantiate:
1. Utility Functions vs. Value Scales
Everyone can use the representation of utility he wants, it just has to be decided whether it's appropriate in the case he applies it to or not. I assume small quantities of every day items (say potatoes) are easier modeled in continuous well-defined functions while preferences for the quantity of shopping malls is much harder to model that way. Neither means the other is necessarily wrong but as always modelling is not the same as reality.
2. Indifference
I can personally see how I am indifferent to a few things but it's unlikely you see it in my actions (other than watching me flip a coin). Now how is that again related to Austrian Economics?
3. Continuity
Basically Mises and Rothbard are arguing against modelling various dimensions as continuous functions. I see how their claim can be true under some circumstances and how it can be useful under others.
So again how is that relevant to being (or not) an Austrian Economist?
4. Welfare Economics
> Rothbard could only claim the welfare effects of government intervention upon "social utility" are indeterminate
Agreed. Government is not necessarily bad.
The rest of the discussion there is about "assumptions": Whether and how a third party affects a voluntary exchange.
Again, this is not at all necessary for Austrian economics, and attacking it is an exercise in futility.
5. Subjectivism
This argument is not an argument, it's about word usage frequencies and how they imply things. WTF