How can one deal with a mosque imam who makes mistakes in reciting the Quran during prayer, knowing that he does not accept guidance and the muezzin of the mosque refuses to intervene?

If this person recites Surah Al-Fatihah correctly and does not commit a clear, meaning-altering error (laḥn jalī), then praying behind him is valid. He has more right to lead the prayer if he is the appointed Imam, and you should pray behind him and advise him gently and kindly. However, if he commits an error that invalidates the prayer (laḥn mubṭil), then it is obligatory to advise and teach him. If he does not learn, then it is not permissible to pray behind him, and his matter must be brought to the attention of the authorities to appoint someone more suitable than him.