Basically it seems that Major Whyte was dying a slow, lingering, horrible death from septicæmia brought on by untreated bedsores, which were a side-effect of a spinal injury he had suffered while hunting three years earlier (ie he had broken his back falling off a horse). He had got interested in Christian Science and so rejected any medical treatment apart from surface disinfection of the wounds. The Crown attempted (and failed) to prove that this was the result of the negligence of Dr Adcock.
There is an impressive roll-call of participants. Ludwig Freyberger, the first doctor called to give evidence, pops up here as a practitioner of newfangled autopsy techniques; he also had a family connection with Friedrich Engels. Sir Victor Horsley, who had performed the original spinal operation, ended up dying in Iraq during the first world war. Another testifying doctor, Henry Huxley, was the son of Darwin's bulldog and therefore uncle of Aldous Huxley and father-in-law of Elspeth Huxley. Captain Fisher, who seems to have brought Major Whyte into contact with Christian Science in the first place, was the incompetent general secretary of the League of Nations Union after the first world war.
Despite the fact that the establishment medics clearly felt Adcock was guilty, the jury was unable to agree (and press reports suggested that only one of them really felt strongly in favour of a conviction). He seems to have been a convincing witness, denying totally that he enjoyed a normal doctor/patient relationship with Whyte, asserting that Whyte was dying in any case and there was nothing that normal medical science (as opposed to Christian Science) could have done, and admitting to his own cocaine habit in a way which seems to have got the sympathy of the jurors.
It's all a long time ago - Major Whyte was my grandfather's oldest brother (born on Christmas Eve, 1864; my grandfather was born in 1880, my father in 1928 and I was born in 1967). It is an odd coincidence that he was the same age when he died as I am now (41).