1) The Midrash asks, “What motivated Korach, who was one of the carriers of the aron, to rebel against Moshe?” Why does the Midrash focus specifically on the fact that Korach helped carry the aron? Chazal tell us that the aron was “nosei es nos’av,” it carried those who were carrying it. Someone who didn’t know better might look at a kohen and say, “There is no way that guy is strong enough or big enough to carry the aron!” That assessment may be right, but it didn’t matter – those selected to do the job were given the ability to do it. The aron schlepped them; they didn’t have the schlep the aron. Korach should have realized that even though when he looked at Moshe, at Aharon, he thought that there is no way they are qualified, it doesn’t matter. “Aron nosei es nos’av” – it’s all about siyata d’shemaya.
2) The Midrash tells us that the wife of On ben Peles sat by the doorway of their tent washing her hair so that no one could enter and involve her husband in the rebellion of Korach. R’ Ya’akov Kamentzky points out an amazing thing. Here you have people leading a rebellion against Moshe Rabeinu, a rebellion that in effect undermined Torah itself by calling Moshe’s credibility into question, and they are makpid not to see a woman's hair uncovered -- they are medakdek on something that plenty of "frum" people would not be so concerned about, while at the same time being kofrim in fundamentals.
The problem with Korach was not a lack of frumkeit. The problem was his vested interest in pursuing his own agenda. When there was no vested interest, he had no problems with dikdukei halacha. The ba'alei musar would tell you that this is no exception to the rule -- it's human nature. All too often rationalizations are just a means to advance an agenda driven by underlying negi'os. The general populace, however, sees a guy who they know is nedakdek on every kutzo shel yud making an argument and so they assume this too is l'shem shamayim and has validity. It's hard to tell the difference.
3) Moshe’s reaction to Korah and his camp is “Rav lachem bnei Levi.” When Moshe davened to enter Eretz Yisrael, Hashem echoed those same words, saying (Devarim 3:26), “Rav lach…” and denied Moshe’s request. What kind of midah k’neged midah is this? The camp of Korach followers wanted to overturn the system and take authority and position that was not theirs. Moshe Rabeinu, as the gemara (Sotah 14) tells us, wanted to enter Eretz Yisrael simply to be able to do more mitzvos. Why should Hashem throw back at him the words he used against Korach?
There was a lot to criticize about Korach’s rebellion, but the one silver lining was that at least some of the participants may have really wanted to be on a higher level of ruchniyus. Sometimes aspirations cannot be fulfilled; sometimes there are boundaries to what one can achieve; however, having she’ifos and dreams of greatness is itself only positive. When Moshe said “rav lachem,” the message he was sending was that you can’t even dream. He shut down the aspirations of those involved without trying to redirect it to some healthier channel. That was what Hashem found unacceptable, and therefore Moshe’s own dreams were held back.