1) The author doesn't bring up the variable of accuracy and genuineness in mediumistic readings. Just how many "revelations" coming through mediums are genuine is difficult to gauge, but without carefully documented validation of each medium's genuineness, the first explanation would simply be that the medium was not actually channeling anybody, but unintentionally stating their own views on the subject (often, views influenced by mainstream Christianity).
2) In the highest state of consciousness, corresponding to the most exalted view of reality, there is no reincarnation and no past or future, as "A Course in Miracles" suggests. However, there are also no chairs, tables, or individual people. So it is useless to bring up this argument to refute reincarnation, unless you are prepared to refute chairs, tables and individual people. In short, in a world where chairs, tables and individual people exist, reincarnation also exists.
3) There is, according to my studies, such a thing as a "group soul," and there is also such a thing as a "soul group," and they are very different. A "group soul" is only found among the most primitive life-forms. A colony of corals, and the blades of grass in the yard, may belong to one soul, and thus the individual parts may belong to a "group soul." This phenomenon may, so far as I understand it, apply even to a colony of ants, or a school of fish (hence, the amazing acrobatics of a school of sardines when chased by a predator). But it definitely does not apply to human beings. There is only one of you incarnate at a time. A "soul group," on the other hand, refers to separate individuals who tend to incarnate together repeatedly.
4) The concept that a human mind has more facets than can express themselves in any one given incarnation, is correct--but this cannot be carried too far. If you have a peak experience, you have access to more of yourself than you do ordinarily. Likewise if you undergo psychotherapy, you may become consciously aware of facets of your personality that were hitherto in your "blind spot." But you do not become a "mega-being" or a totally different person. Meanwhile, in ordinary life, you are not really just one person, anyway. With your sister you are one person; in your job you are someone else, and with your spouse, yet another person. All that happens when a person crosses over, is that these facets are more fully conscious. But to exaggerate this and use it as a refutation of reincarnation as it is commonly understood by reincarnationists, is to abuse the concept. In short, these mediums and/or the spirits they channel are over-using this "facet" concept to further an anti-reincarnation ideological agenda.
The confusion lies in equating the Higher Self, Greater Self, or Oversoul with the mind. This "facet" phenomenon is not a phenomenon of the Greater Self, it is a phenomenon of the mind. The Greater Self is pure Existence. It does not have "facets." The mind, however, is comprised of the mental impressions of a vast number of human incarnations (many of which, however, are similar repetitions). These impressions cannot all find comfortable co-existence in any given human incarnation, though eventually a person learns to integrate them to an increasing degree. That means that a more advanced, experienced person will have access to more facets and can better integrate them. But it is still the same mind which incarnates each time, and the facets overlap. This has nothing at all to do with the Greater Self, because the Greater Self is above the mind and is actually the same in each person, being impressionless. That Silver Birch could make such an error (assuming he is real) points up the fact that people on the other side should not be considered absolute authorities on spiritual matters. In my opinion they should be treated as one might regard a highly intelligent, but still fallible, professor.