Beginning Rosh HaShanah in the middle of the day, if witnesses to the new moon come at that point, as an edict to prevent people from taking that day lightly the next year: Eruvin 39a-b; Beitzah 4b-5b
Considering the two days as a single holiday, or as two separate sanctities: Eruvin 39a, 39b-40a; Beitzah 3a-b, 4b-5b
Treating the two days as a single holiday even after the enactment of R' Yochanan ben Zakkai, lest people err when the rule returns to accept testimony only until midday: Beitzah 5b Separating a tithe and saying that it will take effect on whichever of the two days is not actually the holiday: Eruvin 39a, 39b; Beitzah 3a-b
Prayers
Mentioning in Rosh HaShanah prayers, "If this is the right day, answer me today. Otherwise, answer me on the other day.": Eruvin 39a, 40a
