“They find people who speak the language, and they ask these people to correct them when they make a mistake” is natural. I never thought about it. If you use plural, would that suggest you expect them to make a lot of mistakes?

Generally, if you are asking someone, you would say: Correct me if I'm wrong. Correct me if I make a mistake. It would sound a bit unusual if the asker actually spoke the words: "make mistakes". But if you are writing a passage on this topic you might write: He corrects people when they make mistakes. See the difference?

Thank you Jim Boyce! :-)

sanya, The most natural way would be to say, "They find people who speak the language, and they ask these people to correct them whenever they make a mistake." This suggests that every time they hear a mistake, they will correct it.