The two most obvious instances of misuse of power have been the Japanese internment of WWII and the Watergate scandal of the Nixon administration.
In WWII, President Roosevelt used his powers as commander in chief to order the internment of all people of Japanese descent on the West Coast. This was done without any attempt to determine which people posed a threat to the US and which did not.
In the Watergate scandal, President Nixon used his powers to try to cover up crimes. These were crimes that had been committed in an attempt to help him win reelection.
In both cases, presidents misused the powers that their office gave them.
Misuse of power is a somewhat subjective term. However, across the world, the probability of a leader misusing power increases when people fear for their security in safety. Think of it like a hierarchy of needs. Safety is one of the most essential. So people are willing to forego a lot of their civil liberties because they aren't as essential as safety.
This was certainly the case with Franklin Roosevelt and Japanese internment, where people felt their safety trumped the civil liberties of citizents.
Worldwide, we see evidence of this in France with Napolean. France was (putting it mildly) chaotic at the time, and Napolean brought them stability even if that meant less civil liberties than at any point when France was a monarch. This is also a contributing factor to Hitler and Lenin's (and later Stalin's) rise to power.
In the US, other instances can be heavily debated. People sometimes like to say that the New Deal is an example. Others will say that the Patriot Act is an example of this too.
I think you will see that usually Presidents don't or can't misuse their power unless there is some outside problem that will let the people overlook it.
They may also misuse power if they feel that no one will catch them, but in this day and age, that's less and less possible.