What is the ruling on the imam appointing only one congregant to correct his mistakes, and preventing any other congregant from correcting him, even if that congregant has memorized the Qur’an, and even if this appointed congregant is not present behind the imam?

It is permissible for a congregant to correct the Imam (fath ala al-imam) if the Imam forgets or makes a mistake. This is the position of the majority of scholars and its desirability has been narrated from a number of Companions and Imams, in contrast to those who disliked it, relying on a very weak hadith.

Appointing one person to correct the Imam's recitation is permissible, but if this person is absent, it is not permissible to prevent others from correcting the Imam. The Imam does not have the right to prevent congregants from correcting his erroneous recitation.

Correcting the Imam may be obligatory if the mistake invalidates the prayer, such as forgetting a verse from Al-Fatihah or a melodic error (lahn) that changes the meaning. It may be recommended if it does not change the meaning. If the Imam insists on preventing corrections and conflict is feared, it is permissible to refrain from correcting, unless it is obligatory.