Why is inflation a good thing or bad thing in an economy?

Most economists argue that low and stable inflation is consistent with economic growth but that high or unstable inflation (and especially unexpected inflation) is harmful.
Inflation has numerous costs:
1) Shoeleather costs — this mainly refers to the cost of converting non-cash assets to cash. With high inflation holding cash is costly as high inflation erodes the purchasing power of money. Consider Germany in the 1920s Zimbabwe in the 2000s up to 2009. (Zimbabwe’s inflation was so astronomically high that it stopped printing its own currency in 2009.)
This term could also refer to the inconvenience in general of searching for alternatives and of adjusting to price changes.
2) Menu costs — this refers to the costs of changing posted prices — not just on restaurant menus of course.
3) Distortion of relative prices — this problem is related to menu costs. As firms continuously need to adjust prices (and as consumers continuously need to learn new prices) the adjustments inevitably lead to changes in relative prices that could lead to misallocation of resources.
4) Tax distortions — the simplest example is bracket creep. If we set income tax rates based on income levels (as we do in the U.S. and in many other nations) inflation will cause all income levels to creep into higher marginal tax rate brackets. This can happen with any tax based on progressive marginal rates.
5) Arbitrary redistribution of wealth — unexpected inflation changes the costs and benefits of any fixed contract especially those of long-term duration. The simplest example is the distribution between lenders and borrowers but any fixed contract with obligations could suffer the same type of redistribution. In the case of a fixed-rate loan the borrower benefits (and the lender suffers) from an unexpected increase in inflation because the repayment has a lower value than expected.
It is worth noting that significant deflation has very similar problems. Generally low and stable inflation minimizes these costs and accommodates economic growth. The real problems come from instability (lack of predictability).