Miriam was one of the 7 prophetesses whose prophecy was recorded: Megillah 14a
Miriam was also known as Efrat and Azuvah: Sotah 11b-12a
Miriam was a sickly child, leading people to abandon her, and giving her the name, "Azuvah." Kalev married her and built her up, to the point where she became beautiful: Sotah 12a
Miriam and the birth of Moses
Miriam's prophecy on the birth of Moshe, and the fulfillment of that prophecy: Megillah 14a; Sotah 11b, 12b-13a
Amram returned to his wife, Yocheved, on the advice of his daughter, Miriam: Sotah 12a
Amram's rationale in separating from Yocheved, and Miriam's response: Sotah 12a
When Moses was born and the house filled with light, Amram kissed Miriam's head and said, "Your prophecy is fulfilled!" Then when Moses was thrown into the sea, Amram slapped her and said, "Daughter, where is your prophecy now?!": Sotah 13a
Miriam waited for an hour to see whether her brother would be all right (in his ark on the river), and so the Jewish people waited seven days for her while she was leprous, and did not travel without her: Sotah 9b, 11a
When the Torah describes how Miriam waited to guard Moshe, the verse also refers to Gd's Manifestation [Shechinah] being there, too: Sotah 11a
Miriam went to get a midwife for Moshe with alacrity, like an adolescent girl: Sotah 12b
Miriam didn't tell Batyah that she was Moshe's sister, and was bringing Moshe's mother: Sotah 12b
Marriage to Kalev
Because Kalev married Miriam with pure intent, he was considered to have "birthed" her: Sotah 12a
Explanations of more names of Kalev - Yashar, Shovav, Ardon, Ashchor, Avi, Tekoa - as they relate to his relationship with Miriam: Sotah 12a
Miriam's Leprosy
Whether Aharon got Leprosy along with Miriam: Shabbat 97a
Miriam's Death
Whether Miriam died with a "kiss" from Gd: Moed Katan 28a
Miriam's death helped the community attain Forgiveness for its sins: Moed Katan 28a