Name some of the legal restraints on police action, and list some types of behavior that might be considered abuse of police authority

Probable cause. An officer has reason to believe that a crime may be comitted. (physical evidence, observations, statements, video/audio.)

Searches. Officers are only allowed to do a pat down (terry search, frisk) as a protective measure. They can do a full search if a suspect is taken into custody.

4th amendment protects against unreasonable search and seizures.  

When a suspect is being questioned (for incriminating information) they must be read their Miranda rights before proceeding. Basic questions are allowed. ("How are you doing?").

Abuse of police authority could be requesting to see an ID when there is no probable cause.