What is it called when a cop arrests you for a perfectly legal activity?

Depends on your jurisdiction ... in general, in the United States, a sworn police officer has authority to place you under arrest and take you in to custody.  Upon arrival at processing (jail) someone might determine that there is no chargeable crime and you will be released.  Please know that "false arrest" is a civil tort and is not applicable to a sworn officer. 

Probably wrongful arrest.

It's called a "mistake."

Im Allowed to & My Judge lets me. Is one of there big yelps on that. & great truth to it in the U.S.  Cops there love to operate on personal I don't likes & to H@ll with the laws. 

false arrest or wrongful arrest are crimes regardless of who arrests you