The mirror = the Word. The word speaks of the Old Testament.
When we look into the Word, we see, literally, the "heart of our birth". The longer one looks at the mirror, the more we begin to see our flaws, blemishes etc. (Some talked about when we see ourselves on video, the camera doesn't lie . . . or how about the great 360 mirror on What Not To Wear? Nothing is hidden. . . ) The mirror - the Word - allows us to look at ourselves but also to gaze upon the face of God.
So we have 2 pictures - one person who "looks at their face in the mirror and, after looking at it, goes away and forgets what he looks like." The 2nd picture we get is a person who "looks intently into the perfect law that gives freedom and continues to do this."
The first person may have scripture memorized, know the books of the Bible, know stories, etc. They have accumulated knowledge but clearly, that is not enough!
The second person is gripped by what they see in the mirror - and keeps on looking! The "perfect law" refers to the OT Scriptures and the teachings of Jesus because he came to fulfill the law. They see the sin in themselves and they also see the holiness of God. Like Paul says in Romans 7:24, "What a wretched man that I am! Who will rescue me from this body of death?"
Which kind of person are we? Do we look into the mirror and act upon what we see? Are we a part of a process of looking & doing, looking & doing, looking & doing?
If we are looking and doing? How is this lived out for you?
James closes with a beatitude: if we hear and do the word, one will be blessed in ALL they do. (Wow, really??) That's what the scripture states . . . :-)