Suppose you adopted Feldstein's perspective that those individuals who fully expected to get back their old jobs soon are not really unemployed, but should instead be viewed the same way we treat workers who remain employed but work shorter hours. If you subtract temporary layoffs from the number of unemployed, here's what the adjusted unemployment rate would look like. The earlier recessions look much more like the recent jobless recoveries.
What Hamilton is suggesting is that it has always the case that workers on temporary layoff have been recalled quickly, while permanent job losses have been replaced slowly. In recent recessions, the mix between temporary and permanent job losses has been different, so on average the recovery in employment has been slower.
Hamilton passes along a tax-based explanation for this. That is, our tax laws used to subsidize temporary layoffs, but they no longer do so, because unemployment benefits are now taxed. Instead of a tax-based explanation, I think that the key factor is a change in industry structure. We no longer have a large portion of the economy subject to the sort of inventory fluctuations that give rise to temporary layoffs and recalls.
Note that if temporary layoffs should not be counted as unemployed, then earlier postwar recessions would be revised to appear much milder than they did at the time, at least in terms of the unemployment rate.