The discussion of the Sign of Peace comes towards the end of the video clip in the section of the DVD about the Liturgy of the Eucharist. The text that accompanies the video clip, and the relevant part of the accompanying essay, has this to say about the Rite of Peace:
The Communion Rite continues with the Rite of Peace, the rite by which the Church asks God to grant peace and unity to all her members as well as to the whole human family. This prayer is followed by a symbolic gesture in which all in the assembly exchange a greeting of peace with those around them. The greeting is conveyed in words and through a sign: a handshake or embrace or kiss which is an expressionof the genuine desire that all may be at peace. The gesture is symbolic in that those nearby in the assembly with whom the peace is exchanged represent all those whose lives touch our own and with whom we need to be at peace. In the words of one Father of the Church:There are aspects of this catechesis that I find helpful and informative, but there is also a key one that I would wish to express more strongly, though it touches on a point beyond my control and beyond the control of the good sister who gives the catechesis in the video clip. Rather than saying that "whatever gesture is chosen for this rite should be dignified" - that could be said about going on stage to collect an Oscar - I think the issue is that "whatever gesture is chosen for this rite should be sacred", something implied when the exchange of peace is described as a "solemn religious action". It is not intended to be the everyday greeting that we give in the streets or at our places of work, and one can be forgiven for seeing the examples shown on the video accompanying this section of sister's catechesis as being rather everyday though carried out with some reverence. At a time when not a few are adopting the "orantes" gesture or holding hands during the praying of the Lord's Prayer, I do wonder whether the introduction of the new translation does not give Episcopal Conferences an opportunity to adopt a new gesture for the sign of peace, something akin perhaps to the Liturgical kiss of the high Mass in the Extraordinary Form, a gesture that is clearly sacred in character.
"This kiss that all exchange constitutes a kind of profession of unity and charity that exists among them. Each of us gives the kiss of peace to the person next to him, and so in effect gives it to the whole assembly because this act is an acknowledgment that we have all become the single Body of Christ the Lord and so must preserve with one another that harmony . . . loving one another equally, supporting and helping one another, regarding the individual’s needs as the concerns of the community, sympathising with one another’s sorrows and sharing one another’s joys (Theodore of Mopsuestia, Baptismal homily 4.39)."
Those with whom we exchange the peace also represent the entire world community whom we, as followers and messengers of Christ, pray may experience the peace that only Christ can give. The Rite of Peace has three parts: first, the prayer for peace by the Priest; next, his wish for peace to all those gathered in the assembly, and finally, the greeting and gesture of peace among all those taking part in the Mass. It is up to the Bishops of a given territorial Conference to determine the gesture suitable for the exchange of peace in accord with the culture of their people. The exchange of peace is a solemn religious action and whatever gesture is chosen for this rite should be dignified and carried out in a reverent manner.
I found the identification of the three parts of the Rite of Peace useful - it is all too easy to take the exchange of the sign of peace among the congregation as being the complete Rite - and the prayer of the priest for peace gives a clearly Christological orientation to the "peace" that is exchanged. I also found the ecclesial (as opposed to a merely social) implication of the sign of peace, illustrated by the citation from Theodore of Mopsuestia, useful. It isn't just about "being friendly to someone next to you in Church"; it is about the person to whom you offer the sign of peace being representative of the Church as whole. The representative nature of the exchange also makes sense of a directive to exchange the sign only with the person nearest you in the Church - there is no necessity to exchange the sign with as many as possible. When the Rite of Peace is seen as a whole, its Christological-Ecclesial dimension is more readily appreciated.
I suspect, though, that it will take a lot of persistent catechesis before most of the faithful at Mass on Sunday come to appreciate the true meaning of the Sign of Peace. Cynically, one might insert "clergy included" after the word "faithful" in the last sentence - but my experience suggests that such an insertion is less cynical and more realistic than it would appear.