Unemployment rates ignore 'frustrated workers' who would normally be considered thse who have given up their job search due to a prolonged lack of success. Canada recently had the unusual, but entirely possible situation of an increase in both the employment rate of the general population, and the unemployment rate of those who identified themselves as 'in the work force'. Effectively, enough frustrated workers resumed their job search to make the unemployment rate increase, even though job creation far out-stripped population growth in the period.
Under-employment should be a concern at almost any level. It means the economy is not producing efficiently because it is wasting resources that could be employed to greater effect elsewhere. It may be a matter of semantics if someone is working a relatively good job, but is qualified for another that pays a little more or is a little more porductive. University grads managing gas bars would be a legitimate concern though, and that seems to be the sort of thing that's a little more prvalent todya than five or six years ago (not an exclusively American problem; lots of countries including Canada have the same phenomenon causing problems).
Frictional unemployment is unavoidable, at some relatively low rate. I would go far enough to say 5.6% actual unemployment would be pretty reasonable, since it means roughly 6-8 months of job search for every 20 years of employment. That is hardly unusual, even for highly qualified, capable employees. The reported unemployment rate is however always biased lower than the actual rate by discounting frustrated workers, unemployed students and the underemployed. The real rate is much harder to calculate.