Whether Shabbat depends on some form of sanctification by the Courts: Kiddushin 37b
Rabbi Yochanan ben Zakkai's edict that the witnesses should always go to a central location, regardless of where the Chief Justice is: Rosh HaShanah 31b
How many judges are needed: Rosh HaShanah 25b [2x], Ketuvot 21b, Sanhedrin 2a
Moshe and Aharon acting as the first court for declaring the New Month: Rosh HaShanah 25b
The court's verdict stands, even in error, even intentionally in error: Rosh HaShanah 25a
The time of day when testimony is accepted: Beitzah 5a; Rosh HaShanah 30b
After the Temple, there was still a need to break Shabbat in order to establish the month at a proper time and avoid a juxtaposition of Holidays and Shabbat in such a way as to cause problems in burying people or preserving food: Rosh HaShanah 20a
Breaking Shabbat to bring one witness: Rosh HaShanah 22b
"Beit Yazek," where the witnesses stayed if they arrived on Shabbat: Rosh HaShanah 23b
Months of 30 Days vs Months of 29 Days
The "secret of adding [to the calendar]": Rosh HaShanah 20b
Maximum number of months during the year which may have 29 and 30 days: Rosh HaShanah 6b