A patient exchange can teach more than a correction delivered with embarrassment.

A correction that arrives with embarrassment attached teaches two things at once, and the feeling outlasts the fact by years. People remember the flush of being caught out long after the detail has gone, and they become more careful about speaking rather than more accurate. A patient exchange keeps the person present, which is the only condition in which anyone learns anything. Being right is easy, and leaving someone able to continue is the harder part.

Correct things inside a conversation rather than as an event. Give the information without an audience, and keep talking afterwards.