The Prophet (peace and blessings be upon him) said, “The one to lead the people [in salah] should be the best of them in reciting the Book of Allah“. Therefore, it is the duty of the Muslim community to select for Mosques the best qualified to undertake the responsibility of leading Muslims in Prayer. Thus, when there is an imam who is bad in his recitation, he should be advised to learn the correct rules of recitation and should even be helped in this regard. If he is an official imam, complaints should be submitted to the officials to replace him with a qualified one. Also, you may look for a masjid in which a good imam leads the prayer and pray with him.
Here, we would like to quote Sheikh Muhammed Salih Al-Munajjid, who said,
Correcting the imam is divided into two categories:
Obligatory correcting, which is to correct the imam concerning something which would invalidate the Prayer if done deliberately. So, if he makes a grammatical mistake which changes the meaning of al-Fatihah, then he must be corrected, because this type of mistake which changes the meaning of al-Fatihah invalidates the Prayer. Similarly, if he omits a verse of al-Fatihah, he must be corrected, because that invalidates the Prayer.
Recommended correction, when the imam makes a mistake which does not invalidate the Prayer altogether, but it does undermine the perfection of the Prayer. So if the imam forgets to recite another surah after al-Fatihah, arousing his attention to this is recommended.
The evidence for that is the hadith of the Prophet (peace and blessings of Allaah be upon him): “I am a human being like you, I forget as you forget. If I forget, then remind me.” (Bukhari). So he commanded them to remind him. On one occasion when he became hesitant in his recitation, he said to Ubayy ibn Ka`b, “What stopped you?”, i.e., what stopped you from correcting me? This indicates that correcting the imam is something required.