Is there any form of backbiting that is permitted in Islam?

Summary

Backbiting, which is mentioning about a fellow Muslim something he dislikes, is originally forbidden. Islamic law permits it only for a valid and legitimate purpose that cannot be achieved otherwise. Imam al-Nawawi lists six cases: complaining to a ruler or judge when wronged, helping to oppose wrongdoing, seeking a fatwa from a mufti, warning and advising Muslims, speaking of someone who sins openly, and mentioning a well-known trait such as blindness or muteness. Using such a trait with the intent to insult remains forbidden.

Written in our own words from the original fatwa — check the source before acting on it.