What are the connotations of "Rav lachem" and "u'Madu'a Tisnas'u al K'hal Hashem?
Rashi: 'You have taken for yourselves more than your fair share of greatness; If you (Moshe) took for yourself the kingship, you should not have picked for your brother the Kehunah!'
Seforno: Refer to 16:3:2:2 ... 'and why did you therefore block the Bechoros from performing the Avodah, inasmuch as you first acted as Kohen Gadol during the Shiv'as Yemei ha'Milu'im and then appointed Aharon as Kohen Gadol permanently?
What did Korach mean when he said "Kulam Kedoshim"?
Rashi (from Tanchuma): He meant that all of Yisrael were on the same footing, since they all heard Hashem's voice on Sinai.
Ramban (on Pasuk 19): He meant that the Avodah should revert to all of Yisrael, as it was originally. 1
Rashi writes that all of Yisrael were Kadosh, for they all heard Hashem's voice on Sinai. Only Moshe was able to hear all Aseres ha'Dibros!
Gur Aryeh: We cannot explain simply, that it says "v'Hiskadeshtem vi'Hyisem Kedoshim" (Vayikra 11:44), for this is not a reason not to be a leader over them. Rather, we all heard Anochi and Lo Yihyeh Lecha from Hashem, so we do not need someone else between us and Hashem. 1
Sifsei Chachamim citing Nachalas Ya'akov: Granted, it is proper that you (Moshe) be king, for you heard all Aseres ha'Dibros. However, Aharon is no better than the rest of us! Why did vou pick him to be Kohen Gadol?
Erech Apayim 1 (va'Yosef Avraham 20): Korach admitted that Moshe and Aharon raised Yisrael from the 49th level of Tum'ah to a great level. However, now that they are at a great level, they do not need Moshe and Aharon, rather, they blemish them, like Parah Adumah, which is Metaher the Tamei and Metamei the Tahor.
Why did he say "uv'Socham Hashem"?
Alshich: Do not say that we were Kadosh, but lost this at Chet ha'Egel. Hashem commanded us to build a Mishkan and dwell among us!
How could Korach demand Kehunah even for Zarim, e.g. On ben Peles was not a Levi?