On what date did Yom ha'Shemini fall?
What is it the eighth day of?
Rashi: It was the eighth day of the Milu'im. 1
Sifra: Not the eigtht day of the month ? since the Torah wrote in Tzav, 8:33 "Ki Shiv'as Yamim Yemalei es Yedchem".
The 'Hey' in "ha'Shemini" implies that the day was a special one. In what way was it special?
Rashi: It was special inasmuch as it took ten crowns - as listed in Seider Olam (and in Shabbos). 1
Megilah, 10b: Hashem rejoiced on it to the same extent that He rejoiced when the world was created ? which we learn from a Gezeirah Shavah "Vay'hi" "Vay'hi Erev Vay'hi Voker".
Shabbos 87b: It was one of ten firsts: The first day ... 1. of the creation, ... month of the year, ... 2. of the inauguration of the Mizbe'ach at the hands of the princes, ... 3. of the Kehunah, ... 4. of theAvodah in the Mishkan, ... 5 that fire descended from Heaven to burn the Korbanos, ... 6. that the Kohanim ate Korbanos. ... 7. day that Bamos were prohibited, ... 8. that the Shechinah descended to the Camp of Yisrael, ... 9. that the Kohanim blessed Yisrael. Moshav Zekenim - a hint to this is va'Yehi. The letters spell 'Yud Hayu' ... 10. of the twelve months.
Why did Aharon and his sons need to be called?
Oznayim la'Torah: Because at the end of Tzav Moshe had said to them "Ki Shiv'as Yamim Yemalei Hashem es Yedchem", and those seven days had now terminated.
Why did Moshe call the elders of Yisrael?
Rashi: He called them to hear that Aharon was entering the Kehunah Gedolah as per Divine instructions, and not of his own accord. 1
Da'as Zekenim and Rosh: It was to raise Aharon's esteem in their eyes.
Why did the Shechinah not descend until the eighth day?
Moshav Zekenim: Due to the principle 'Midah ke'Neged Midah'. For seven days, Hashem asked Moshe to go to Mitzrayim, and on the seventh day, Moshe said "send the one that You will send." Correspondingly, for seven days Moshe thought that the Kehunah is his 1 , and on the eighth day, Hashem told him to call Aharon. 2
Why did Moshe not call all of Yisrael?