This passage occurs in the Narrative Lectionary Year 1 (most recently Nov 9, 2014).
Summary: The inclusion of chapter 5 allows one to see Gospel in chapter 6, namely, that fulfillment of the law (so beautifully summarized in 6:6-8) will ultimately not depend on humanity but on God acting in Jesus Christ, his first born son, who will shepherd the people. I spend a lot of time considering justice, especially within the context of Micah.
עלה ("olah" meaning "burnt offering", 6:6): I realize that discussion of ancient Jewish offerings is not intuitively interesting. But the this type of offering has significance here. In a burnt offering, nothing is left for the people. Normally an offering to please the gods allowed for fat to burn for the gods, and meat for the humans. But in a burnt offering to God, nothing was left over. In short, it is a total sacrifice, leaving no food behind for either the one making the sacrifice or even the priest. The section in 6:6-8 should not be dismissed to lightly. The world and ourselves are fundamentally broken to enter into the presence of God.
םשפט ("Mishpat" meaning "justice", 6:8): The word justice has a very broad meaning in the Hebrew Bible. What does it mean in this case?
Perhaps a way to get at its meaning in Micah is too look at examples of injustice that the prophet cites:
Micah 7:3 Their hands are skilled to do evil; the official and the judge ask for a bribe, and the powerful dictate what they desire; thus they pervert justice.
Corrupt rich people; violence:
Micah 2:2 They covet fields, and seize them; houses, and take them away; they oppress householder and house, people and their inheritance.
Micah 6:11-12 Can I tolerate wicked scales and a bag of dishonest weights? Your wealthy are full of violence; your inhabitants speak lies, with tongues of deceit in their mouths. (See also mountain of the Lord that brings peace).
Micah 3:10-11 who build Zion with blood and Jerusalem with wrong! Its rulers give judgment for a bribe, its priests teach for a price, its prophets give oracles for money; yet they lean upon the LORD and say, "Surely the LORD is with us! No harm shall come upon us." (See also 3:5)
Micah 5:13-14 and I will cut off your images and your pillars from among you, and you shall bow down no more to the work of your hands; and I will uproot your sacred poles from among you and destroy your towns.
First point: God cares about justice in that he both expects people to behave with justice and will punish injustice.
Second point: For God, justice includes a totality of how society is oriented, especially toward those who lack resources.
Third point: Just about everyone, it seems, is commiting injustice.
I think the ethical imperative for us to live an honest and fair life is clear. The question comes down to, however, how we try to promote, do or make justice beyond ourselves. I think it is fair to say the imperative here is not simply a personal dictate to live an honest life, but to ponder, pray and act about injustice in the whole of society. This for me is a very humbling task, one that makes me want to walk humbly and with God.
אהב ("Ahav" meaning "love", 6:8): This word means "love" much like we use it in English -- it covers a great deal of things and relationships. It is also used in Deuteronomy 6:5, where the Israelites are called to love God with the heart, soul and strength, perhaps a nice way to think about this verse. This verse is the prophetic conversion of the command to love our God into the command to love our neighbor. It has always been there, but now it is made clear.
צנע ("tsana" meaning "humble" (as verb), 6:8) This verb only appears once in the Hebrew Bible. Thus, not gonna say too much. But I think its worth considering the other verb, walk -- in that this is a full body action, governing our entire sphere of action. God wants the totality of society, but also the totality of our own actions, to be in line with his will.