How does unethical behavior affect the perception of law enforcement among the public?
Policing is based to a great degree on trust. A society could never have enough police officers to prevent crime if people did not police themselves and serve to deter other people from committing crimes. If police officers are not trusted by the community, much of this self-policing stops being effective. For example, if someone sees a crime being committed but does not trust the police, that person may not report the crime or come forward as a witness at a trial.
A specific area in which this has become an issue right now is the problem of racial profiling and associated police brutality which have aggravated the already fraught relationship between police forces in large United States cities with members of ethnic minorities. This leads to a vicious cycle in which members of racial minorities, aware of the bad behavior of a small minority of racist police officers, become distrustful of the police, leading to less community cooperation with law enforcement.