So, this requires a little background.

Manly P. Hall (1901-1990) got his start as a preacher in 1919; his mother had been involved with occultism and the young Hall delved deep into pretty much every form of religion, magic, and mysticism he could get his hands on, according to Master of the Mysteries: The Life of Manly Palmer Hall. His personal charisma and erudition attracted patrons with deep pockets, who financed his travels and deeper learning. One of the products of this was publication, and his magnum opus was Secret Teachings of All the Ages (1928), which wasn't quite as all-encompassing as Lewis Spence's An Encyclopaedia of Occultism (1920), but pretty lengthy.

Secret Teachings of All the Ages can basically be summed up as a gloss of the history of (mostly) Western occultism; Hall uncritically condenses and regurgitates the apocryphal myths of the founding of the Freemasons, the Rosicrucians, and other groups. This differs from contemporary movements like Theosophy in that Hall doesn't really synthesize a lot of this material, at least not to the same degree as the theosophists did, and makes little pretense of having new revelations beyond unveiling all the legends and lore he's already put together - which is, to be fair, no small feat.

For a comparison, you might look at my answer on I’d like to know more about the Theosophy movement. Hall does cite a few theosophists in Secret Teachings, but doesn't seem to have absorbed the full text of The Secret Doctrine or Isis Unveiled, or at least doesn't make the effort to fully incorporate Theosophy into his accounting of the occult history of the world, picking and choosing bits that suit his thesis.

Refuting any individual part of the book isn't necessarily difficult, but it's almost entirely a mishmash of legends and ideas that had already been in circulation for years or centuries, so the sheer amount of material to be refuted can be a little daunting. For example, if you look at Hall's chapter on Atlantis, it is basically a summary of those myths and ideas about Atlantis which were then current, especially leaning in on Ignatius Donnelly's Atlantis: The Antediluvian World (1882). My answer to How did the Atlantis myth begin? hits on most of the key points from the early part of Hall's section on Atlantis; the only difference being that Hall assumes Atlantis was real to some extent despite the original evidence clearly showing it's fictional, and keeps on going.

Which is really characteristic of a many occult writers of the period. There are too many claims in any given amount of text to do a full debunking of each one, and even trying to do that quickly becomes tiresome. While Hall isn't particularly good with his citations in this volume, most of the works he does cite or quotes aren't accredited histories but other occult compilations, the Bible, antiquated anthropological texts, etc. Much of the book simply summarizes or restates material from other books; the section on Ceremonial Magic and Sorcery for example is basically just a gloss of the work of Eliphas Levi.