Why is price dispersion from Inflation called relative price “distortion”?
The word "distortion", (as used in e.g. the Ramsey–Boiteux pricing), is not intrinsically negative.

It simply means that people change their consumption behaviour because of changes in price(s).

For example, a tax on oxygen would not (and cannot)  be distortive because people have no choice but consuming oxygen.

A contrario, a tax on tabacco is distortive, and is actually precisely implemented because of this very trait: it will change the consumption behaviour of smokers.

Put differently, the notion of distortion is strongly related to the notion of price elasticity. 

Also, constraining markets equilibrium can generate deadweight losses, which is likely the reason why people think of the word "distortion" as negative. Is changing behaviour via price signals negative per se? Is trying to make people quit smoking negative per se ? No.


The word "distortion" is probably one of the most misconceived/misused notion in economic theory, especially when it is used in the political sphere. But originally it has, I repeat, no negative connotation. And I really think that this is how Mankiw uses/perceives it.




  Why is price dispersion from Inflation called relative price “distortion”?


It is called so because consumption behaviors do not change if all increases of prices in the economy are of the same relative magnitude $\iff$ the dispersion is null. E.g. a tax on, say, tobacco, has to be distortive to be useful, i.e. it has to be greater than inflation, even if such intervention can actually generate deadweight losses.