Is it permissible for worshipers to debate and argue in the mosque if the Imam makes a mistake in some hadith, and what is the appropriate conduct in such cases?

If the Ahadith mentioned by the Imam are fabricated or weak, and they pertain to beliefs (Aqa'id) or rulings (Ahkam), then it is not permissible for him to mention them. And whoever hears him should advise him gently. However, if they are weak and pertain to the virtues of deeds (Fada'il al-Amal), then there is no harm in him mentioning them, provided certain conditions are met, as permitted by the majority of scholars.