The leprosy or “marks” in garments mentioned in the latter portion of chapter 13 are probably mold or mildew. If they wash out, fine, if not there’s a problem that needs to be taken care of. As elsewhere, if water doesn’t do the trick, use fire!
It might aid in understanding 14:5 for one to realize that literally running water is “living water.” This should also make us think of Jesus and his message of living water in John 4–He IS that living water!
Log (of oil) in 14:15 is a unit of measure approximately equal to a pint. The term atonement used in this section means “to cover over.” In other words the sin is covered over so that it is no longer visible–as if it were not there at all. This is important later in the New Testament. Be aware that there are those who try to say that atonement means “at-one-ment.” This is a heretical teaching with no basis in Scripture.
The laws regarding the cleansing of a “leprous” house are obviously referring to bad mold (14:33ff.). We’ve heard a lot about this in recent years.
Psalm 26, David says Vindicate me Oh Lord, for I am walking in Your ways! Examine me and see if I’m not pure. Remember that David is the king and therefore has an even greater role as a good example for his people than does the average person.