(Updated video link 3/11/2013)
John 20:21 - before He grants them the authority to forgive sins, Jesus says to the apostles, "as the Father sent me, so I send you." As Christ was sent by the Father to forgive sins, so Christ sends the apostles and their successors forgive sins.
John 20:22 - the Lord "breathes" on the apostles, and then gives them the power to forgive and retain sins. The only other moment in Scripture where God breathes on man is in Gen. 2:7, when the Lord "breathes" divine life into man. When this happens, a significant transformation takes place.
John 20:23 - Jesus says, "If you forgive the sins of any, they are forgiven. If you retain the sins of any, they are retained." In order for the apostles to exercise this gift of forgiving sins, the penitents must orally confess their sins to them because the apostles are not mind readers. The text makes this very clear.
Matt. 9:8 - this verse shows that God has given the authority to forgive sins to "men." Hence, those Protestants who acknowledge that the apostles had the authority to forgive sins (which this verse demonstrates) must prove that this gift ended with the apostles. Otherwise, the apostles' successors still possess this gift. Where in Scripture is the gift of authority to forgive sins taken away from the apostles or their successors?
Matt. 9:6; Mark 2:10 - Christ forgave sins as a man (not God) to convince us that the "Son of man" has authority to forgive sins on earth.
Luke 5:24 - Luke also points out that Jesus' authority to forgive sins is as a man, not God. The Gospel writers record this to convince us that God has given this authority to men. This authority has been transferred from Christ to the apostles and their successors.
Matt. 18:18 - the apostles are given authority to bind and loose. The authority to bind and loose includes administering and removing the temporal penalties due to sin. The Jews understood this since the birth of the Church.
John 20:22-23; Matt. 18:18 - the power to remit/retain sin is also the power to remit/retain punishment due to sin. If Christ's ministers can forgive the eternal penalty of sin, they can certainly remit the temporal penalty of sin (which is called an "indulgence").
2 Cor. 2:10 - Paul forgives in the presence of Christ (some translations refer to the presences of Christ as "in persona Christi"). Some say that this may also be a reference to sins.
2 Cor. 5:18 - the ministry of reconciliation was given to the ambassadors of the Church. This ministry of reconciliation refers to the sacrament of reconciliation, also called the sacrament of confession or penance.
James 5:15-16 - in verse 15 we see that sins are forgiven by the priests in the sacrament of the sick. This is another example of man's authority to forgive sins on earth. Then in verse 16, James says “Therefore, confess our sins to one another,” in reference to the men referred to in verse 15, the priests of the Church.
1 Tim. 2:5 - Christ is the only mediator, but He was free to decide how His mediation would be applied to us. The Lord chose to use priests of God to carry out His work of forgiveness.
Lev. 5:4-6; 19:21-22 - even under the Old Covenant, God used priests to forgive and atone for the sins of others.