Why we add a second day even though we know which one is the right day: Beitzah 4b
We only add a day after the day we assume to be the right one, not before it: Rosh HaShanah 20b-21a
Locations where a second day is required: Rosh HaShanah 21a Ex-Communication for travelling on the Second Day: Pesachim 52a
Consuming New Produce on the 17th of Nisan, which may -due to the calendar doubts- be the 16th: Menachot 68b
Considering the two days as a single holiday, or as two separate sanctities: Eruvin 39a, 39b-40a; Beitzah 3a-b, 4b-5a
Enactments to prevent people from taking the second day lightly: Eruvin 39a-b, 40a
Performing Havdalah after the first day: Beitzah 4b [see Shitah Mekubetzet there] Taking care of a corpse on the second day of Yom Tov: Beitzah 6a Respect for all creatures vs. the status of the rabbinically-decreed second day of Yom Tov: Beitzah 6a
Respect for all creatures overridden by concern that it could lead to greater disruption of Jewish law: Beitzah 6a
