Inflation is costly in a social justice sense, because it arbitrarily redistributes wealth among different groups in society. Not only does inflation blunt the link between effort and reward, it typically hits hardest those who can least afford it.
Inflation is also costly because it obscures the relative price signals that must come through clearly if the economy is to adapt to change and make the most of opportunities for growth. At present, high oil prices should be encouraging energy efficiency and alternative fuels development. High dairy prices should shift land use towards dairy production.