Moshe Rabbeinu performed avodah in the Mishkan for the Shivas Yemei Ha-Miluiim, but the Shechinah did not yet rest in the Mishkan; only when Aharon began his avodah did the Shechinah come. (Talmud Yerushalmi - Yuma 1:1, per Torah Temimah) Why did Moshe's avodah not merit the presence of the Shechinah? Surely, Moshe was just as committed to Hashem as was Aharon, and Moshe was not a party to the Chet Ha-Egel; why, then, did his service not accomplish hashra'as ha-Shechinah?

Moshe's avodah in the Mishkan was quite unusual. It not only occurred at the time of inauguration and celebration of the newly-constructed Mishkan (it was during the Chanukas Ha-Mishkan), but it also required that Moshe assemble and dismantle the Mishkan each day. One can suggest that the contrast between Aharon's avodah and that of Moshe provides insight as to why it was the avodah of Aharon which merited hashra'as Ha-Shechinah.

Unlike the avodah of Moshe, Aharon's tasks in the Mishkan were not part of any celebration. His Mishkan service was routine, and upon entering into his avodah, Aharon knew that he was about to embark on a lifetime commitment of regularity. (This is perhaps symbolized by the finality of Aharon's avodah, in which the Mishkan was no longer assembled and dismantled each day, for Aharon's service was of a permanent nature.)

It is the commitment to regular, routine service of Hashem which brings the Shechinah. Only after the excitement and celebration were over and a permanent, day-in and day-out system of avodah was implemented did Hashem cause his Presence to dwell in the Mishkan. This is the beauty of Aharon's avodah.

Aharon's avodah was special not only in terms of its inherent quality but in its timing as well. Rashi quotes many ma'amarei Chazal which teach that Aharon's meek attitude toward being chosen for avodah ba-Mishkan and the subsequent hashra'as ha-Shechinah are to be viewed in the shadow of the Chet Ha-Egel, such that the acceptance of Aharon's service indicated that Hashem forgave his role in that tragic event. I think that this means that Aharon's service - which embodied personal humility and subservience to the divine routine - was a contrast to the haughtiness and subjective actions of those who worshipped the Egel, in which they used their own personal aspirations and imperfect human logic to determine how to conduct themselves religiously.

In this same light may we understand the tragic and severe demise of Aharon's sons, Nadav and Avihu, whose deaths occurred immediately after Aharon commenced his Mishkan service. Rather than performing avodas Hashem devoid of personal, subjective actions, as was the lesson of the Egel and Aharon's avodah, Nadav and Avihu took the avodah somewhat into their own hands, performing acts in Hashem's service which they subjectively thought would enhance it. (According to the opinion that their sin was that they rendered p'sak in the presence of Moshe, the same logic applies, as they felt that they could convey the d'var Hashem better or more quickly, albeit without license.) Not properly applying the thematic lesson of the Chet Ha-Egel and defying the foundation of avodah ba-Mishkan on the very day of commencement of Mishkan service, Nadav and Avihu were hence punished with unusual severity. 

The latter part of the parshah presents the halachos of animal and plant life vis a vis tumah and taharah. Upon the pasuk, "To separate between that which is tamei and that which is tahor..." (11:16), Rashi invokes the words of Toras Kohanim, "To distinguish between most of the windpipe being slaughtered (so as to render the animal kosher) and half of it being being slaughtered (which would result in a treifah)". This idea - and the balance of the latter section of the parshah - teach that tumah and taharah, and Torah as a whole, are defined by Hashem, and the slightest deviation changes the entire picture. This lesson of deviation versus subservience to Hashem is the glue which joins the parshah's themes into one.