Is it obligatory to correct the imam when he repeatedly makes mistakes in reciting the Qur’an, changing the meaning, or changing words without changing the meaning, knowing that he rejects advice and it is difficult for the mosque administration to replace him?

The Imam should only be prompted if he makes a mistake in recitation (laḥn), not if he recites with a mutawātir (concurrently transmitted) qira'ah (recitation variant), such as reciting (وأن الله ربي وربكم) with an alif (i.e., wa 'anna Allaha rabbi wa rabbakum), because this is the qira'ah of Nafi', Ibn Kathir, and Abu 'Amr. Prompting the Imam is permissible for a mistake that does not alter the meaning, and obligatory if it alters the meaning. Leading the prayer by someone who frequently makes mistakes (al-laḥḥān) is disliked but his prayer is valid, and praying behind him is valid even if he makes many mistakes. The Imam is advised to be gentle and lenient, and one of the respected figures can be assigned to offer him advice.