As a priest Jesus Christ cared for people and dealt with their sin compassionately. The priestly role is all about caring for hurting people.
The priest has a deep understanding of human suffering and they are compassionate and merciful in tending to the needs of hurting people so that they are loved to spiritual maturity. Priests are masters at resolving conflicts between people so that there is reconciliation through the Gospel.
The weakness for a priest can be that they are so people focused that they tend to be disorganized. They can run from crisis to crisis without building other leaders and systems to care for people in large numbers. Priests can also be merciful and patient to the point of enabling people in their sin and not calling them to an urgent repentance.
The content of this post leans very heavily on the teaching of the folks in the following organizations: The Resurgence, The Gospel Coalition and Desiring God. Pastor Jamie Munson spoke on this topic awhile back … you can find the audio here: http://theresurgence.com/2010/12/13/prophet-priest-king