Assalaamu alaykum. In our area, whenever an imam makes a mistake, like standing after the second unit of prayer without sitting for Tashahhud or sitting for Tashahhud after the third one, people behind him make Takbeer (saying: Allahu Akbar [Allah is Most Great]), instead of Tasbeeh (saying: Sobhaan Allah [glory to Allah]) to make him aware. Is that allowed? And as for those who make Takbeer, will their prayer remain valid?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

If anything happens during the prayer, then the Sunnah for the worshipers is that the men say Tasbeeh and the women clap their hands.

Nevertheless, it is permissible to draw the attention of the imaam with something other than Tasbeeh, such as Takbeer , Tahleel (saying: La Ilaaha illa Allah [there is nothing worthy of worship but Allah]), and the like, and this does not invalidate the prayer. However, it is better to make Tasbeeh in order to follow the Sunnah.

Ar-Rawdh Al-Murbi' and its commentary read:

“It is disliked to attract the attention of the imaam by coughing or clearing the throat, whistling, or clapping (for men), or for the women to say Tasbeeh; but it is not disliked to attract his attention by recitation (of Quran), Tahleel, Takbeer, and the like, such as saying Tasbeeh, Tahmeed (saying: Alhamdulillah [praise be to Allah]), Istighfaar (saying: astaghfiru Allah [I seek forgiveness from Allah]), as this is permissible because this is of the same kind of speech as the prayer. The same applies when the imaam forgets a Thikr (expression of remembrance of Allah) and the person led in prayer raises his voice with that Thikr in order to remind him, and so forth.”

Allah knows best.