"Why do neoclassical economists oftentimes blame only two factors on unemployment: (i) wage rigidity or (ii) a rise in the disutility of labor? What year are we in, 1936?"
I would say, "what year are we in, 1935?". I'll explain further down. Jonathan's alternative* is to think about productivity and the structure of production:
"Elaborating on why lack of education might not play as big a role in unemployment as some suggest, [Jonathan just finished discussing skills mismatch ideas] imagine the labor market from a Hayekian perspective. There is a total supply of labor with heterogeneous skills. The labor supply is drawn from by firms looking to achieve some rate of income, but there is an ambiguous degree of inflexibility in the ability to mix labor and capital. Two simple alternative ways of looking at this problem include having to demand capital goods that are complimentary to labor or training labor to become complimentary to a given stock of capital goods. In reality, both may occur, as well as other methods of mixing the two. What this means, though, is that entrepreneurs have certain expectations and understandings given the available stock of capital, labor, and the expectations they hold on the future state of demand (relative to their output). This suggests that the structure of production will have to, in part, be shaped around the specificity of labor. Otherwise, we would see a permanent historical trend of discoordination between entrepreneurs and the supply of labor."
The important question, Jonathan suggests, is "what is holding back productivity?".
I think that's basically right, but the way we talk about labor productivity can be misleading, I think. "Productivity" is output per worker at a point in time. Giving a worker a job is really an investment. Labor isn't purchased on a spot market. It's a weird investment that the investment good (labor) can walk away from and that gets (sort of) renegotiated at regular intervals. But it is like an investment insofar as employers are thinking about a stream of future earnings from the job, and not just what the worker is producing at a given point in time.
Jonathan, I think, is right to note the heterogeneity of labor, and thus its complementarity with capital and expectations about the available capital stock (it's that last bit that really connects it to the Austrian school). But the fact that the "productivity" that employers really care about is a forward looking expectation of future earnings from a given worker also makes this a very Keynesian reorientation away from more modern friction stories (not that those friction stories are bad... they just might not be complete).
Jonathan also spends a lot of time talking about "real" constraints on productivity, which I of course also think are relevant.
* I'm not prepared to immediately dismiss sticky wages. The "adjustment has to occur on the employment margin" point is fairly obvious, but it's also just an explanation for why the aggregate demand curve is downward sloping. I thought I had a post on that but I can't seem to find it.