What is the ruling on the prayer of someone who forgot a prostration (sajdah) in the third rak’ah of the Asr prayer, then was alerted by the worshippers, so he completed the prayer and performed the prostration of forgetfulness (sujood as-sahw)? Then opinions differed between the prayer being invalid and needing to be repeated, and completing the prostration then the tashahhud and tasleem, and between one who completed his prayer with five rak’ahs?

After the Imam's salām, you could have rectified the prayer by performing a rak'ah in place of the third rak'ah from which the Imam omitted a prostration. The third rak'ah would then be nullified and replaced by the fourth. Your previous prostration of forgetfulness (sujud al-sahw) would have sufficed. As for the congregants who were certain about the omitted prostration, they should have said "Subhanallah" to the Imam. If he did not understand, they should have spoken to him as necessary. If he still did not comply, they should have performed the prostration themselves. If they followed him in omitting it, their prayer would be nullified. As for those who joined late (al-masbooqūn), what they did is correct and their prayer is, Allah willing, sufficient if they performed a rak'ah after the Imam's salām, provided they were unaware of the prohibition of following the Imam in standing before performing the second prostration.