Quote: It looks to me like you have faces with vertices that need to be welded. I would go into the source file and check the areas that appear to be "tearing" and see if this is the case. Even if all of the verts are weighted, two adjacent faces with vertices not welded will mean that the faces are not sharing an edge. This could result in what I saw in your video.
I fixed the chest and neck tears simply rigging again the whole area. There was a problem with the vertex as you guess about.