The Ohr haChaim (32:1) writes that the Torah only alludes to the murder of Chur by the eigel worshippers, but spells out in great detail all aspects of the cheit ha'eigel itself because the story of cheit ha'eigel is not about the tragedy of sin, but rather is about the possibility of redemption. Chazal (A"Z 4b) tell us that if the community sins they should remember the cheit ha'eigel, as it teaches us the possibility of communal teshuvah. The sin of Chur's murder was never atoned for, and so, rather than leave the blot on the record of Klal Yisrael, the Torah only alludes to it in passing. Klal Yisrael did do teshuvah for the cheit ha'eigel, and therefore the Torah makes it the focal point.
"Ra'isi es ha'am ha'zeh v'hinei am k'sheh oref hu" -- can there be a more damning statement than that? The Ishbitzer (in Beis Ya'akov), however, turns the statement on its head. The navi (Chavakuk 1:13) tells us that G-d is "t'hor einayim mei're'os ra v'hibit el amal lo tochal." G-d cannot bear the sight of evil; he will not look at it. "Ra'isi es ha'am ha'zeh," G-d tells Moshe that he sees Bnei Yisrael -- despite their sin, he still is looking at them. Their essence is still pure. Again, the story the Torah is telling us is one of redemption.
Coming back to Chur (and if someone can explain why he deserved to die, please leave me a comment), the gemara (Sanhedrin 7) explains that it was the sight of his being killed by the mob that led Aharon to make the eigel. "Im yei'hareig b'mikdash Hashem kohen v'navi," the murder of a kohen and navi together (true, Har Sinai is not the mikdash and the avodah had not yet been given over to kohanim -- see Maharasha) together are unforgivable. Aharon thought that with Chur the navi killed, if he protests against the mob and they kill him, it's all over. The eigel was in this case the lesser of two evils.
Why is that so? Why is killing a navi and kohen together a more heinous crime than even idol worship? Maharasha explains that the kohanim are the teachers of Torah and the nevi'im convey the dvar Hashem. They are the bearers of the mesorah. It is one thing to have a mesorah and to do wrong, even to the point of idolatry. It's a far worse thing to completely destroy and eradicate that mesorah.
So the people sin, and Moshe comes to the rescue with his tefilah. "Zechor l'Avraham l'Yitzchak ul'Yisrael... v'kol ha'aretz ha'zos... etein l'zarachem v'nachalu l'olam." Moshe calls on the zechus of the avos, and refers specifically to G-d's promise to grant Eretz Yisrael to them and their children for eternity. Why would that promise carry weight after the people had sinned? The Avos were always worried "shema yigrom ha'cheit" and they would prove undeserving -- wasn't Moshe worried that the cheit ha'eigel may have made the people undeserving? See Seforno, Netziv, and perhaps one could argue that Klal Yisrael as a whole can never be completely undeserving as a nation (see R' Tzadok in Pri Tzadik on the parsha of the bris bein ha'besarim). R' Yonasan Eibshitz says a beautiful yesod to answer his question. He writes that it's only in Eretz Yisrael that we can truly come to be zocheh in Torah. That was the purpose of promising the land to the Avos and their descendants. Moshe was telling G-d that since the Jewish people have not yet come into Eretz Yisrael, since that promise was yet unfulfilled, how then can he blame Klal Yisrael for their wrongdoing? How can he hold them accountable for a breach of Torah when all they have learned is the Torah of galus and have not yet experienced the real thing?
Baruch Hashem, we are on the road to getting back to the real thing and need to take advantage.