All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Uttering Tasbeeh (i.e., saying, “Subhaana Rabiyy Al-‘Atheem (How perfect my Lord is, the Supreme)” or, “Subhaana Rabiyy Al-A’la (How perfect my Lord is, the Most High)”) three times in bowing and prostration is not obligatory on the person led in the congregational prayer. What is obligatory is saying Subhaana Rabbiy Al-‘Atheem once when bowing and uttering Subhaana Rabbiy Al-A`laa, once in prostration. The ruling is same for an Imaam, the one led in prayer and the one who performs prayers individually. See Fatwas 92193 and 88987.
As for leaving out the Tashahhud (the supplication said whilst seated in prayer) for the one being led in prayer, if it is the first Tashahhud, then there is no harm. The scholars have clearly stated that if an Imaam stands for the third Rak’ah (unit of prayer) before the follower (the one led in prayer) completes his Tashahhud, then it is allowed for the one being led to stand before completing the Tashahhud.
If the questioner means that the follower did not complete the final Tashahhud, then this Tashahhud is one of the pillars of the prayer. If he does not perform this Tashahhud by the time the Imaam concludes the prayer with Tasleem (i.e., saying, “Assalaamu ‘Alaykum” at the end) and he also concludes his prayer following the Imaam without saying the final Tashahhud, then his prayer is not valid, and he has to repeat his prayer because he has omitted a pillar of the prayer. The least Tashahhud that would suffice for the person led in prayer would be to say, “Attahiyyaatu lillaahi, assalaamu `alayka ayyuhan-nabiyyu wa rahmatullaahi, assalaamu `alaynaa wa `alaa ibaadillaahis-saaliheen. Ash-hadu allaa ilaaha illallaah, wa anna Muhammadan `abduhu wa rasooluh (or anna Muhammdan rasooluhu). (Glorification is for Allaah. All acts of worship and good deeds are for Him. May Allaah exalt your mention, O Prophet. Peace be upon us and all of Allaah’s righteous slaves. I bear witness that none has the right to be worshipped except Allaah and I bear witness that Muhammad is His slave and Messenger.)”
If the questioner means that one does not complete “As-Salatul Ibraaheemiyah (prayers upon prophet Ibraaheem and upon the Prophet Muhammad, sallallaahu ‘alayhi wa sallam)”, after the Tashahhud, then this is also one of the pillars of the prayer according to the predominant view of the scholars, as we mentioned in Fatwa 85656. This pillar would be sufficed by merely saying, “Allaahumma salli `alaa Muhammadin” while saying complete As-salatul Ibraaheemiyah is merely recommended (but of couerse, preferable). If the follower concludes his prayer with Tasleem following the Imaam after saying this part only, then his prayer would be valid.
Allaah Knows best.