There are many harmful aspects of monetary inflation. The obvious (although not to all) effect is that prices rise. In other words, over the long term, monetary inflation leads to price inflation.
Monetary inflation is a redistribution of wealth. It benefits debtors at the expense of creditors. It benefits those holding hard assets (at least during the artificial boom stage). It hurts consumers. It tends to hurt wage earners, except those in industries who see the money first. It hurts savers.
As taught by the Austrian Business Cycle Theory (ABCT), monetary inflation leads to a boom and bust cycle. The loose money, and typically artificially low interest rates, leads to massive distortions. It makes certain things appear more profitable than they really are. It sends false signals to the marketplace, making it appear that there is more savings and capital than what really exists.
In relation to this last point, inflation misallocates resources. It directs resources towards things that would not otherwise be done. So while inflation redistributes wealth, it also reduces the overall wealth. The net effect is that it makes the average person poorer, or at least worse off than he would have been without the monetary inflation. Inflation harms productivity.
Inflation is also what allows the federal government to spend such massive amounts of money. Without the Fed buying government debt, there is no way that the government could spend such vast amounts. The marketplace probably wouldn't buy the government debt without demanding higher interest rates. And vastly higher taxes would be unlikely. Therefore, without inflation from the central bank, government spending would be much lower. Since almost all government spending is a misallocation or resources, monetary inflation enables much higher government spending.
Of course, we also wouldn't have the massive national debt without the ability of the Fed to create new money out of thin air. While I don't think the overall debt is the most important thing, it correlates to the massive spending that makes our standard of living far lower than it should be.
This is important to remember, because even if you make some good financial decisions and investments, and seem to benefit from inflation, it is still making your worse off. It is just that you will be less worse off than those who did not prepare properly and trusted their government with a monopoly over the money they use.