In this chapter, the LORD gives even more commands regarding the guilt offering, and then summarizes what parts of the various offerings the priests are allowed to eat.
The first thing I noticed reading this chapter is that in verse 2, the LORD equates sinning in a variety of ways (chiefly related to stealing or lying for the purpose of material gain) to "act[ing] unfaithfully against the LORD". To steal someone's property is unfaithful towards the LORD. This is an interesting perspective, and perhaps shows us why the Law of Moses, ostensibly a religious document, contains moral laws at all. I mean, after what we've read, I think everyone can understand why the covenant, a lordship treaty between God and the Hebrew people, precludes "religious sins" like idolatry or profaning the name of the LORD.
However, the ten commandments implies a peculiar equivalence between the first five "religious" commands (having another god before the LORD, idolatry, revering the name, obeying the Sabbath, honoring parents) and the last five "moral" commands (do not murder, steal, testify falsely, commit adultery, or covet). I think one could reasonably ask, why does the LORD care about "moral" behavior that is interpersonal (i.e. between you and another person) and does not involve sinning against him?
This chapter equates stealing to acting unfaithfully, but that's possibly just a reference to the commandment. That is, since "not stealing" is part of the covenantal agreement, stealing is simply a violation of the covenant. So this verse doesn't really answer the question I raised above, why the LORD cares about interpersonal actions.
I'm not going to fully answer this question here; I think there are a lot of ways to look at it, some of which are even correct (that's a joke). I will offer one perspective and otherwise leave this as an exercise for the reader: I believe this all goes back to the pre-Curse world of Eden, that before sin entered the world and Adam and Eve were drive out, there was no interpersonal strife like we see in the ten commandments. I have written many times that the Covenant is a reversal of the curse of Adam, and we have seen how it protected the Israelites from the plagues in Egypt, including the plague of death, which I equate to the threatened death of Genesis 3. It stands to reason, then, that the various commands in the covenant are also part of the reversal by commanding the Israelites to not do the things that are a direct result of the curse, such as murder.
Of course, since murder is a result of volition and not divine judgment (like the flood of Noah or the plagues of Egypt), it is perhaps more fair to equate murder with the sin of Adam rather than the curse of Adam. In that sense, commanding the Israelites to not murder is a parallel to God's command to Adam not to eat the forbidden fruit. At the end of the day, the reason for not murdering will always seem tautological because God simply commands it without explanation, just as eating the forbidden fruit is prohibited without explanation. By analogy, it is impossible to "think outside the box", i.e. outside of a given moral system, if you "live inside the box", i.e. live in a universe in which that moral system holds. If anyone wishes to disobey these commands, then they must risk living outside the protective boundary of the covenant.
Moving on, we should compare verses 2 through 5 with Exodus 22, which also concerns property rights. It's interesting to note that the penalty, the "extra" that must be returned, is much, much lower here than it was in Exodus. Exodus was concerned primarily with the theft of livestock, and the penalty there varied from double to five times what was stolen (if the thief is no longer in possession). Here, the penalty is 20% of what was stolen. I don't know why there is such a big difference, other than perhaps livestock theft was much more common considering the livestock would spend most of their time outside grazing, and also considering how important livestock were to the Israelite economy.
In addition, the person must make a guilt offering (which was not commanded anywhere in Exodus). It is important to note that this chapter talks about "incurring guilt" and not about "becoming unclean". Because of this, and other reasons, I think theft is pretty clearly a moral sin. However, in the last chapter I explicitly noted that the guilt offering was primarily related to ceremonial cleanliness, so this is a bit of a contradiction. This mixed usage of the guilt offering is one reason why I am hesitant to consider moral sin and ceremonial uncleanliness to be fully separable. At the same time, the last chapter never told us what the guilt offering was for; I was simply trying to infer it based on context. It appears that the guilt offering is a bit vaguer than I made it sound last chapter.
Next, we are told what parts of the sacrifices the priests are allowed to eat. This is largely in conformance with what we have already read. We also see that the bronze altar is to be kept burning always, much like the altar of incense and the golden lampstand within the tabernacle itself.
As before, the burnt offering is mostly destroyed, and therefore unprofitable to the priest. Since a burnt offering is usually paired with a grain offering, they at least have that.
Lastly, the regulations governing the sin offering are repeated, consistently with before. If you recall chapter 4, there were some sin offerings where it was to be burnt outside the camp (the offerings for the high priest and the congregation) and some where only the fat was to be burned (offerings for a leader or the common people). In the second case, we are now told that the priest is allowed to eat of it, but that it is most holy (a ceremonial designation) and it is variously restricted for that reason. The part about breaking earthen vessels and scouring bronze vessels is just about keeping the "holiness" of the sacrifices within the confines of the tabernacle, i.e. to prevent those vessels from being used outside of the tabernacle and accidentally making other things holy.
As before, the reason to "keep the holiness within the tabernacle" is because holiness cannot mingle with things that are not holy. That's why the Israelites washed before encountering the LORD in Ex 19, that's why the LORD refused to go with Israel after their sin in Ex 33:3 (but then later changed his mind).
The subject of offerings continues in the next chapter.