According to hadith of Rasool salal laho aliehi wasalam a Muslim man or woman who hides the fault of another Muslim will be favoured by Allah on the day of judgement in the way that Allah swt will hide his faults on that day.
However we can expose someone in some specific Situations which are following:
1 A person has violated a hudd & evidence is needed in court.
2 A person‘s ideology is dangerous for masses.
3 A person is twisting message of Quran & Sunnah.
4 Some one is going to be selected as a groom & relatives of bride need to know about him.
5 Someone is an office bearer /leader and has misused public property /resources Otherwise we need to be silent & should hide fault of others.
So we should be hiding faults of our brothers and sisters from others and if we want correct those faults we should to talk to them in loneliness about it.