How can one reconcile the Prophet's not ordering Mu'awiyah to repeat his prayer after he said "Yarhamuk Allah" (May Allah have mercy on you) to one who sneezed during prayer, even though he was ignorant of the ruling, with his ordering the one who prayed badly to repeat his prayer, even though he was ignorant, which indicates the invalidity of his prayer in both cases?

The hadith (definition) of Mu'awiyah ibn al-Hakam indicates that the ignorant person is excused for speaking during prayer, as the Prophet (peace and blessings be upon him) did not command him to repeat the prayer, but rather taught him the prohibition of speaking therein in the future. As for the hadith of the one who prayed incorrectly, it indicates the necessity of repeating the prayer for one who omitted commanded actions in prayer out of ignorance; because he was commanded to repeat his prayer despite his ignorance of the correct manner of prayer. The difference between the two cases is that Mu'awiyah committed a prohibited act (speaking), whereas the one who prayed incorrectly omitted a commanded act (pillars of prayer). Therefore, the ignorant or forgetful person is not held accountable for committing a prohibited act if he did not intentionally violate it, but he is obliged to rectify the omission of a commanded act whenever possible.