The first point here is that inflation problems go hand in hand with stong wage growth. In the high inflation period of the 1970s, wage growth was never less than 7.5% per year. Strong wage growth in the late 60s preceded the slide into high inflation. Inflation is a problem that tends to appear in the late stages of an economic boom, not when the economy is deeply depressed. Wage growth at present is very low.
The second point is that the Fed's current target for inflation, at 2.5%, is far lower than the 3-5% inflation that prevailed during Reagan's presidency. Nobody saw inflation as a problem at the time, even though it was far above the level which the Fed now regards as acceptable. And job growth in the Reagan recovery was far better than anything which we have seen in the past few years.
Clearly the Bernanke Fed has prioritized low inflation over fighting unemployment. I believe this reflects a lack of accountability to the American public.
Wage growth isn't likely to be a problem any time soon
This chart shows wage growth in blue and the unemployment rate in green. Wages seem to take off when unemployment gets below about 5%. There is no chance of that happening in the near future because unemployment remains far too high. If wage growth stays low, so will inflation.