And all the praises and thanks be to Allah, Lord of all that exists.
means, praise be to Him at the beginning and end of all things. Because Tasbih (glorification) implies a declaration of being free from all shortcomings, the two ideas appear together here and in many places in the Qur'an.
Allah says;
سُبْحَانَ رَبِّكَ رَبِّ الْعِزَّةِ عَمَّا يَصِفُونَ
وَسَلَمٌ عَلَى الْمُرْسَلِينَ
وَالْحَمْدُ لِلَّهِ رَبِّ الْعَالَمِينَ
Glorified be your Lord, the Lord of Al-`Izzah! (He is free) from what they attribute unto Him! And Salam (peace!) be on the Messengers! And all the praises and thanks be to Allah, Lord of all that exists.
Sa`id bin Abi `Arubah narrated that Qatadah said,
"The Messenger of Allah said;
إِذَا سَلَّمْتُمْ عَلَيَّ فَسَلِّمُوا عَلَى الْمُرْسَلِينَ فَأَنَا رَسُولٌ مِنَ الْمُرْسَلِين
When you send Salam on me, send Salam on all the Messengers, for I am one of the Messengers."
This was recorded by Ibn Jarir and Ibn Abi Hatim.
Abu Muhammad Al-Baghawi recorded in his Tafsir that Ali, may Allah be pleased with him, said;
"Whoever wants a greater measure of reward on the Day of Resurrection, let him say at the end of any gathering,
سُبْحَانَ رَبِّكَ رَبِّ الْعِزَّةِ عَمَّا يَصِفُونَ
وَسَلَمٌ عَلَى الْمُرْسَلِينَ
وَالْحَمْدُ لِلَّهِ رَبِّ الْعَالَمِينَ
Glorified be your Lord, the Lord of honor, glory and power! (He is free) from what they attribute unto Him! And Salam (peace!) be on the Messengers! And all the praises and thanks be to Allah, Lord of all that exists."
Other Hadiths concerning the expiation for any wrongs that may have occurred during a gathering prescribe saying the words;
"Glory be to You, O Allah, and praise. There is no God except You; I seek your forgiveness and I repent to you. "
I have written a chapter dealing exclusively with this topic.
This is the end of the Tafsir of Surah As-Saffat. And Allah, may He be glorified and exalted, knows best.