What is the validity of the Tarawih prayer if the Imam makes a mistake and stands up for a third rak'ah, and the congregants say "SubhanAllah" to him, but he continues his prayer and then brings a fourth?

If the Imam intends four rak'ahs in Tarawih, his prayer is valid according to those who permit it. However, if he intends two rak'ahs then forgets and stands up for a third, he must return and perform the prostration of forgetfulness (sujud al-sahw). Imam Ahmad explicitly stated that standing for a third rak'ah in the night prayer is like standing for a third rak'ah in the Fajr prayer, as the night prayer is performed in sets of two (mathna mathna), based on the Prophet's (peace be upon him) saying: "The night prayer is two by two." The Imam must return immediately if he is alerted, even if he has started reciting. Then he sits, says the taslim, and performs two prostrations for forgetfulness. Similarly, the follower (ma'mum) does not continue with the Imam if he proceeds in his prayer; rather, he sits for the tashahhud, intends to separate from the Imam, and says the taslim.