Why was the section on the Menorah put next to the section on the princes [the end of parshat Naso]? Because when Aharon saw the inauguration by the princes he became unhappy, because neither he nor his tribe participated. God said to him: 'I promise your lot will be better than theirs, since you light and prepare the [Menorah] lights.' " (Rashi to 8:1)
Why, in this story, is Aharon in particular upset at being left out? Why not Moshe, or Miriam, or Korach, or anyone else from the tribe of Levi?
I think the clear answer is that Aharon was the prince of the tribe of Levi. All of his fellow princes participated in the inauguration, and so far he is the only one left out.
(It is also helpful in other places to say that Aharon was the prince of Levi. For example, after the Golden Calf sin in which Aharon participated, you'd think he would be the very last person to be chosen as high priest. It seems therefore that he is not chosen on his own merits, but rather in his role as leader of the tribe of Levi. Also, he is older than Moshe and thus would seem to have priority over him in terms of tribal leadership.)
I am inclined (despite parshablog's probable condemnation) to take this midrash non-literally, as a "teaching tool" designed to explain why these particular laws of the Menorah are located where they are. Immediately after the Menorah laws, we have the ceremony in which the tribe of Levi is consecrated. It seems that the lighting of the Menorah, and this consecration of the Levites, together represent a 13th offering from Levi, similar to the other 12 tribes' offerings in parshat Naso. Conceivable, the whole Levi ceremony even took place on the 13th day after the erection of the Mishkan.
Hashem spoke to Moshe, saying: "Make yourself two silver trumpets; of hammered work you shall make them. You shall use them for calling the congregation together, and for causing the camps to travel. When they blow [VETAK'U] with them, all the congregation shall gather themselves to you, at the entrance of the Tent of Meeting... And when you blow an 'alarm' [TERUAH], the camps that lie on the east side shall travel..." (10:1-2)
These lines indicates the two purposes of the trumpets in the desert. The first purpose - gathering the entire people at the Mishkan - is accomplished by blowing a "tekiah". The second purpose - signaling the beginning of a journey - is accomplished by blowing a "teruah".
Next, we have instructions for using trumpets after entering the land of Israel. Once again, two purposes are listed. When we go to war, we are to blow a "teruah", and on holidays we are to blow a "tekiah" while offering sacrifices in the Temple.
Going to war, and celebrating a holiday in the Temple, are very similar to the two purposes listed in the desert: causing the camps to travel, and gathering the people at the Mishkan. And it's no coincidence that both war and travel require a "teruah", while gathering and holidays each require a "tekiah".
The parallel between these two sets of trumpet-blowings is intriguing. There is also a distinction which may shed light on the relation between them. In the desert, the trumpets were purely functional - there were a couple million people in the camp, and if God suddenly informed Moshe that it was time to travel or receive prophecy, there had to be some way of informing everyone. In contrast, use of the trumpets in Israel is purely symbolic. In both cases in the land of Israel (war and holidays), there is no practical consequence, but rather God promises to "remember" Israel.
What exactly is being remembered? And why was there no "remembering" when the trumpets were blown, on very similar occasions, in the desert? I think that both questions can be answered by saying that God remembers Israel's desert experience. As the prophet Yirmiyahu later wrote, "Thus says Hashem: 'I remember for you the affection of your youth, the love of your wedlock; how you followed Me in the desert, in an unsown land." (2:2) Our willingness to follow God in the desert, whether to battle or to a prophetic encounter, is remembered in our favor when we blow trumpets in similar circumstances in the land of Israel.
Later in our parsha, we find the well-known lines of "Vayhi binsoa ha'aron": "When the Ark travelled, Moshe would say: 'Arise Hashem and scatter your enemies; may those who hate you flee from before you.' And when it rested he would say: 'Return Hashem [to/with] the myriad thousands of Israel'." (10:35-36) Here too, travel is a time for Divine assistance in war, and stopping is a time for encounter with God. This is the idealized picture of our desert experience, even if in practice we were not always able to live up to it.
Hashem said to Moshe: "If her father had spit in her face, would she not be shamed seven days? Let her be shut out from the camp seven days, and after that she shall be brought in." Miriam was shut out from the camp seven days; and the people did not travel until Miriam was brought in. (12:14-15)
The Miriam/tzaraat story takes a weird twist here. Moshe has just prayed that she be healed. God answers that she indeed will be healed, but she must be nevertheless "shamed" for one week. The connection between tzaraat and shame is not obvious. Also, while Miriam is outside the camp the entire people is prevented from traveling. Why didn't they simply travel and Miriam keep up with them, as was most likely the case whenever any other person got tzaraat and had to leave the camp? (See Bamidbar 5:1-4 where lepers must leave the camp - seemingly as a preparation for the journey.)
I think the answer is that Miriam's real punishment was not tzaraat, but "shame". By "shame", I mean embarrassment. The halting of the camp for seven days is a unique punishment designed to embarrass her, with tzaraat merely an technical justification for halting the camp. The entire people is forced to wait for a week for no practical reason but only, as they presumably find out, "because Miriam sinned". This is in fact poetic justice; her offense was defaming Moshe, and now she herself is defamed in front of the entire people.
It has been claimed that the punishment here is unfair, in that both Miriam and Aharon sinned but only Miriam seems to be punished. There are a number of possible answers to this. For example, the text seems to indicate that Miriam was the main offender, or perhaps that only Miriam spoke lashon hara and Aharon just listened. Alternatively, tzaraat must be diagnosed by a priest, and if Aharon the priest got tzaraat it's not clear who would diagnose him.
If the real punishment was not tzaraat but embarrassment, we can provide another answer to this claim. We said that the people found out that the delay was caused by Miriam's sin. But we can equally say that they found out that Miriam AND Aharon had sinned. Only Miriam was physically punished, but the intense embarrassment which was the real punishment would have affected them equally.