Well, the Church doesn't care what the laity think and they certainly don't care what I think. But, had I been writing this article I would have started with two major points: the notion of 'Christ consciousness' and the New Age belief that Jesus was merely one of many avatars or wise men as opposed to being the Messiah. Also, I would address the concept of 'channeling' and its well known dangers to the psyche and spirit.
They need to streamline this document. New Age is a pan-spirituality which believes "I'm okay, you're okay", there is no 'sin' but all is learning. There's another point to hit. In this document they tried to cover too much territory. New Age actually encompasses some very old teachings which are not new at all. It is very much a cafeteria type spirituality. If the Vatican wants to take issue with other pieces then that needs to be done in separate documents. The things I mentioned are hallmarks of New Age though.
What I forgot to add is I think they need to show how New Age beliefs are incompatible with Christianity and Catholicism in particular. They need to delve deeper into the 'how' and 'why' of it. They need to make their case from the perspective of Tradition and Scripture.