Correcting the mistakes of the imam’s recitation in a soorah other than al-Fatihah
Question

If the Imam makes a mistake in the Qranic Reading after Al-Fatiha, should the people behind him correct him if the meaning did not change as if the Imam used the word " Mumineen instead of Muttaqeen"  
in the second Ayat of Surat Al-Baqarah. What happen if the Imam refuses to correct himself even though he knows he made a mistake, but he thinks it is not necessary to correct himself.Will the Salat be void if the meaning changed and the Imams was not corrected?. Can we correct the Imam if he makes a mistake in Qranic Reading during Friday Kuttbah. How about if he makes a mistake in the explanations saying "Unbeleiver will be in Jannah and beleiver will be in the fire ".
Praise be to Allah.If the imam makes a mistake in his recitation – apart from al-Fatihah – that does not alter the meaning, then you do not have to correct his mistake. This is something that no imam is entirely free from. But it is better to point it out to him after the prayer, because this will help him to remember it. 
But if the imam refuses to correct his mistake even though he knows it is a mistake, then one to the following two scenarios applies: 
1 – If the mistake alters the meaning, and he knows that it is a mistake but he does not correct his mistake after it has been pointed out to him, then you must repeat the prayer. 
But how can you be sure that he realized it is a mistake and was persisting in it?  
But if it is a mistake that does not alter the meaning, then you do not have to repeat the prayer, but you must advise the imam in a kind and gentle manner, and explain that it is not something shameful if the imam forgets something, for the best of Allah’s creation, Muhammad (peace and blessings of Allah be upon him), also forgot, and the Sahaabah who were behind him reminded him, as is mentioned in the hadith. 
Shaykh Sa’d al-Humayd 
With regard to correcting the Jumu’ah khutbah, this is one of the cases in which speaking during the khutbah is permitted, such as if the khateeb makes a mistake in reciting a verse that changes the meaning, such as omitting a phrase from the aayah and so on. In this case the one who corrects him is not regarded as coming under the prohibition on speaking during the khutbah. See al-Sharh al-Mumti’, 5/140.