How does one denounce a person who utters incorrect words in front of a group of people?

First, you must verify that the speech is indeed erroneous before refuting it. If you are certain that it is wrong—for example, if it is backbiting or a clear legal error—then you should forbid the evil with the most appropriate and gentle manner, clarifying the ruling of Islamic law with politeness, while seeking excuses for the speaker, remembering Allah's saying: "And speak to him with gentle speech that perhaps he may be reminded or fear [Allah]."