Can someone call the cops on someone and accuse them of doing something and then the cops keep am eye on them?

Let's turn to commonsense to answer your question. *Puts feet up on desk and emits a condescending sigh* Anyone can call the police to make accusations. The police have an obligation to discern if the accusation has any merit. If they believe there is merit, they are within legal bounds to check out the party that has been accused. Note that the accuser could also fall under surveillance.