What is the ruling on someone who was praying behind an Imam, and the Imam made a mistake, such that the worshiper bowed, thinking that the Imam had bowed, when another person said "Allahu Akbar" to begin prayer, and the worshiper remained in his bowing position until the Imam bowed?

It is forbidden to intentionally bow before the Imam. However, there is no sin upon one who does so by mistake, based on the Hadith (definition): "Indeed, Allah has pardoned for my nation their mistakes, their forgetfulness, and what they are coerced into." The prayer of the one who does this is not invalidated in either case, and he must return to a standing position if he realizes his mistake before the Imam bows.