Can there be too little unemployment for the health of the economy? The cyclical rate of unemployment can be negative, which implies that the business cycle sometimes produces too little unemployment. How can there be “too little” unemployment for the health of the economy?
Let me answer a simpler question first. Is it possible for there to be too little orange juice in the grocery store? Definitely. 

Let's say that the price of OJ is set too low (\$1 per liter) and customers who arrive early in the morning buy all the OJ. Assume that those customers think buying all the OJ is a good deal and they figure they'll enjoy drinking it, but that at regular price (\$4 per liter) they'd buy much less, they wouldn't want any more at those prices, and there would be lots left on the shelves. 

People who arrive later in the day want some OJ at \$4 per liter. If they could find them, the early OJ buyers would happily sell them the OJ at that price and pocket the profit (that follows by the demand schedule I sketched out in the second sentence of the last paragraph). That means that there are deals to be done that would improve the allocation of OJ (there are welfare increasing, Pareto-improving, trades to be made). But the early customers and the late customers have trouble finding each other and so the OJ stays in the early shoppers' refrigerators. 

Just about everything I just said about OJ holds for worker labor. Surprise! If the price of labor is set below the equilibrium price then early buyers purchase an inefficient quantity. Later buyers can't find the workers they need even though the marginal value of those workers is higher than the price at which the early employers bought them. Because (or perhaps I should say if) it is less efficient to look for a job while you have a job, when unemployment is too low workers ended up employed by firms that do not employ them at their highest marginal product. If only alternative employers could be found output and welfare could be improved. In fact, using a Kaldor-Hicks mechanism it is possible to make the new employer, the old employer, and the employee all better off under such circumstances. Thus it is not efficient under production efficiency or welfare efficiency criteria.