Sometimes we mention a wrong information, especially during the opening of the debate, we must correct them, but sometimes we may be embarrassed what you think?
The term "mention", I believe, has intentionality associated with it. Other terms may not have this intentionality, e.g.., "misspeak", "accidentally say", and others. In a situation of "mention", a wise student may actually recognize that the point is incorrect. However, that said, I would make the correction as soon as I recognize my error in all of the above cases..