Reports on sa'i

Sayyiduna Ali bin Abi Talib (may Allah be pleased with him) narrates that he saw the Prophet (peace and blessings be upon him) (during sa'i) with his garment drawn up until it reached his knees.
Abdullah bin Ahmad and Imam al-Bazzar recorded it, and its narrators are thiqat (trustworthy).

Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) narrates: One year the Prophet (peace and blessings be upon him) walked at a normal pace, and one year he ran.
Imam al-Bazzar recorded it. Its chain contains Sa'id bin Bashir, about whom there has been criticism.

Sayyidah Habibah bint Abi Tajrah (may Allah be pleased with her) narrates: I saw the Prophet (peace and blessings be upon him) going between Safa and Marwah. The people were ahead of him and he was behind them, and he was running, so much so that because of the intensity of his running I saw his knees, with his lower garment flapping around them, and he was saying: "Run! For Allah Almighty has made running (sa'i) obligatory upon you."
Imam Ahmad and Imam al-Tabarani recorded it, the latter in al-Mu'jam al-Kabir, where she says: I saw that, due to the intensity of his running, his lower garment was swirling around his stomach and thighs, until I saw the whiteness of his thighs. Its chain contains Abdullah bin al-Mu'ammal, whom Ibn Hibban declared thiqah (trustworthy), and he said: he makes mistakes; others have declared him da'if (weak).

Safiyyah bint Shaybah narrates that a woman told her that she heard the Prophet (peace and blessings be upon him) say between Safa and Marwah: "Sa'i has been made obligatory upon you, so perform sa'i."
Imam Ahmad recorded it. Its chain contains Musa bin Ubaydah, who is da'if (weak).

Sayyidah Tamlik (may Allah be pleased with her) narrates: I saw the Prophet (peace and blessings be upon him) while I was in my upper room. The Prophet (peace and blessings be upon him) was between Safa and Marwah, saying: "Indeed, Allah Almighty has made sa'i obligatory upon you, so perform sa'i."
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir. Its chain contains al-Muthanna bin al-Sabbah, whom Yahya bin Ma'in declared thiqah (trustworthy) according to one report, while a group declared him da'if (weak).

The umm walad of Shaybah narrates that she saw the Prophet (peace and blessings be upon him) performing sa'i between Safa and Marwah and saying: "The low ground (al-Abtah) is to be crossed only at a run."
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir, and its narrators are the narrators of the Sahih.

Sayyidah Safiyyah bint Shaybah (may Allah be pleased with her) narrates that the Prophet (peace and blessings be upon him) said: "Perform sa'i! For Allah Almighty has made sa'i obligatory upon you."
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir. Its chain contains al-Muthanna bin al-Sabbah, whom Yahya bin Ma'in declared thiqah (trustworthy) according to one report, and a group declared him da'if (weak).

Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) narrates: The Prophet (peace and blessings be upon him) was asked, and he said: "Indeed, Allah Almighty has made sa'i obligatory upon you, so perform sa'i."
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir. Its chain contains al-Mufaddal bin Sadaqah, who is matruk (abandoned).

Alqamah narrates: Sayyiduna Abdullah (may Allah be pleased with him) stood on Safa at a cleft in it and said: "By the One besides whom there is no god, this is the standing place of the one upon whom Surah al-Baqarah was revealed, the Prophet (peace and blessings be upon him)."
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir. Its chain contains Yazid bin al-Walid, and I have not found anyone giving his biography.

Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) narrates: The Prophet (peace and blessings be upon him) went out of the mosque towards Safa by the Gate of Banu Makhzum.
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir. Its chain contains Abd al-Rahman bin Abdullah Abu al-Qasim al-Umari; Imam Ahmad said: he is a kadhdhab (liar).

Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) narrates: The Ansar said: "Sa'i between Safa and Marwah is a practice of the Jahiliyyah." So Allah Almighty revealed this verse: "Indeed, Safa and Marwah are among the symbols of Allah. So whoever performs Hajj of the House or performs Umrah, there is no sin upon him in going around them."
Imam al-Tabarani recorded it in al-Mu'jam al-Awsat. Its chain contains Hafs bin Jumay', who is da'if (weak).

Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) says: There is no sin upon him if he goes around them voluntarily, and if someone leaves it, there is no harm either.
Imam al-Tabarani recorded it in al-Mu'jam al-Awsat. Its chain contains al-Abbas bin al-Fadl al-Ansari, who is matruk (abandoned).

Abu al-Tufayl narrates: I said to Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both): "Your people say that the Prophet (peace and blessings be upon him) performed sa'i between Safa and Marwah and that it is a Sunnah." Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) said: "They have spoken the truth. When Sayyiduna Ibrahim (peace be upon him) was commanded to perform the rites, Satan confronted him at the place of sa'i and tried to race him, but Sayyiduna Ibrahim (peace be upon him) outran him."
Imam al-Tabarani recorded it as part of a long hadith, which will come later in the chapter on stoning the Jamarat, if Allah wills; and its narrators are thiqat (trustworthy).

Sayyiduna Abdullah bin Mas'ud (may Allah be pleased with him) narrates: When the Prophet (peace and blessings be upon him) was performing sa'i in the bottom of the valley, he would supplicate: "O Allah, forgive and have mercy; indeed, You are the Most Mighty, the Most Noble."
Imam al-Tabarani recorded it in al-Mu'jam al-Awsat. Its chain contains Layth bin Abi Sulaym, who is thiqah (trustworthy) but a mudallis (one who conceals defects in the chain).

Abd al-Rahman bin Tariq bin Alqamah reports from his paternal uncle that when the Prophet (peace and blessings be upon him) reached a particular place in Dar Ya'la (the narrator Ubaydullah specified which place it was), he faced the House and supplicated.
Imam Ahmad recorded it; he also recorded it from Abd al-Rahman bin Abdullah bin Tariq from his father. Imam Abu Dawud and others recorded it from Abd al-Rahman bin Tariq from his mother. As for this narrator Abd al-Rahman, I have not found anyone who declared him reliable or criticised him. The remaining narrators of this report are the narrators of the Sahih.