Leviticus points reveals blazing shadows of the cross. In the sin offering we are shown the power of sin to pollute, the cost to cleanse sin and the pervasiveness of sin.
When one considers that even unintentional and unknown sin polluted the believer it is clear that no believer in the Old or New Testament can hope to claim to be without sin. But God established a way in which the polluted could come, confessing their sins, and know their sin atoned for and forgiven.
In Leviticus this was by a sacrifice - under the New Covenant we have Christ as a once for all sacrifice - it is because of this that God can be called faithful and just to forgive us when we confess our sins.