What are the ramifications of "Vehitzilu ha'Eidah"?
Rashi (Kesuvos, 15a): We learn from here the principle 'Safek Nefashos Lehakeil'. 1
If a Safek occurs in a Din concerning the death-sentence, Beis-Din rule leniently.
What is the connection between the Kohen Gadol and the Rotze'ach?
Rashi: It is not fitting that the Kohen Gadol, who comes to bring the Shechinah down into the midst of Yisrael - to cause them to live longer, together with the Rotze'ach, who cuts their lives short.
Seforno: Bearing in mind that Galus atones for Shogeg, not all cases of Shogeg are of equal severity - some are more guilty, others less. Consequently, each Rotze'ach requires a time-period in Galus that fits his sin. And Hashem achieves this by arranging the deaths to occur at different stages, 5 some closer to the death of the Kohen Gadol, others, further away, whereas yet others die in Galus before the Kohen Gadol. 6
See Sifsei Chachamim.
Because had he done so, it would not have happened.
Targum Yonasan: Or either of the other two cardinal sins - idolatry and adultery.
Targum Yonasan: And because he failed to Daven on Yom Kipur, he will die that year. Refer to 35:25:2:3.
Which Kohen Gadol is the Pasuk referring to?
Ba'al ha'Turim: It is referring to a Kohen Gadol who was anointed with the Shemen ha'Mishchah, to one who became Kohen Gadol by wearing the eight garments and to one who stood in for the Kohen Gadol on Yom Kipur when he was Tamei and who stood down when he (the Kohen Gadol) returned. 1
Ba'al ha'Turim: That is why the Torah mentions 'Kohen Gadol' three times in the Parshah.
Is it really the Rotze'ach who anointed the Kohen Gadol?
Rashi #1: It is a 'short Pasuk', which is missing the word 'ha'Moshe'ach' (the one who anointed him).
Rashi #2 (citing Makos, 11b): Because if the Kohen Gadol dies and they appointed a replacement before the conclusion of the Rotze'ach's Mishpat in Beis-Din, he may only leave the Ir Miklat when the second Kohen Gadol dies (and the Pasuk is simply referring to the Kohen Gadol who was anointed in his time - whilst he was serving his sentence).