Is one who thought the Imam erred in recitation and corrected him, then it became clear that he himself was mistaken, sinful? And is he sinful if the Imam acted upon his erroneous correction?

You should not have rushed to declare the Imam mistaken. However, since you did so out of ignorance, there is no sin upon you, for the Prophet, peace and blessings be upon him, said: "Indeed, Allah has pardoned for my Ummah their mistakes, their forgetfulness, and what they are forced to do." It is better for you to go back to the Imam and explain to him that he was correct and that you were mistaken. No sin will befall you if the Imam continues to recite incorrectly for the rest of his life.