1) After the cheit ha’eigel the Torah tells us that, “Va’aya’asfu eilav kol bnei levi,” that all the members of the tribe of levi who remained true to Hashem gathered around Moshe to carry out his instructions. Chasam Sofer writes that the Torah emphasizes “all” the bnei levi to include Korach and his supporters, no fans of Moshe Rabeinu (I don’t know why C.S. assumes Korach had it in for Moshe already at this point in time, but that’s what he says.) Even they rallied around Moshe. When it comes to sticking up for kvod Shamayim and rectifying the damage of the cheit ha'eigel, all other disagreements need to be put aside. Love Moshe Rabeinu or hate him, this was not the time for that.
We live surrounded by not one eigel, but by 100 eigels, yet it seems it’s more important for some to argue about internal issues rather than unite in common cause.
2) Commenting on “V’ish al ya’aleh imach,” (34:3) Rashi writes that since the first luchos were given with such public fanfare, it attracted ayin ha’ra and things turned out badly. This second time around Hashem commanded Moshe to come alone, in private, as there is no virtue greater than tzeniyus.
If tzeniyus and privacy is such a great thing, then why didn’t Hashem do things that way the first time around? Why l’chatchila make a big show of things, opening the door to ayin ha’ra, and only then, once the price has been paid, change course?
Sefas Emes explains that things had to be done b’davka in this order. You can be a poor kollel couple and eat noodles every night for dinner, but nobody serves noodles at the chasunah. You have to start out of the gate with a bang, with excitement, with fireworks. A rocket ship needs an enormous boost to get it off the ground. Later on, once it's in orbit, a little thrust is all it needs to keep going or to adjust course. Whatever the risks -– ayin ha’ra or anything else -- the first luchos had to be given in way that would shake the world, with fireworks and pomp. An impression had to be created. Once that stage was passed, and only once that stage was passed, could the value of tzeniyus be invoked to temper things the second time around.
3) Rashi (30:36) writes that the Torah mentions the chelbina, which had a foul odor, in the middle of the other ketores spices to teach that “al yakeil b’einecha,” one should not be troubled by the fact that sinners are included in the tzibur on a ta’anis, i.e. their prayers are of value as well. The implication is that of course it would be better if the whole tzibur were tzadikim and the sinners weren’t there, but don’t let it bother you if things aren’t like that. Maharal in Gur Aryeh points out that Chazal put it a little differently and stress the affirmative: “kol ta’anis she’ain bah poshei yisrael aina ta’anis.” (Kerisus 6) It’s not that we merely tolerate sinners, as Rashi implies -- Chazal are telling us that we need and want the sinners there. Why? Maharal explains that ta’anis demands contrition. The further someone is away from Hashem, the more contrite they will be when they return.