I can say something on the disease bit. Although these kinds of armchair posthumous diagnoses can be pretty dodgy to say the least, the research in this case has been published in some leading journals. The dominant theory is one first advanced by Macalpine and Hunter in 1966, and their 1968 follow-up of acute intermittent porphyria modified to variegate porphyria in the follow-up. Which is a hereditary genetic disorder in the synthesis of heme molecules, leading to them building up and causing a whole bunch of issues. This was on the basis of described symptoms including nausea, constipation, abdominal pain and urine discoloration, in addition to the neurological symptoms such as mania and hallucinations/delusions. The main dissent today is a professor TJ Peters, who's criticized Macalpine's evidence and argued in favor of a diagnosis of bipolar disorder. (1, 2, 3, 4, pdfs )

Peters points to the weakness of the urine color evidence - Macalpine listed four references to the urine being variously 'bilious', 'darkened', 'bloody', leaving a 'blue ring' on a container and 'bluish'. As had been pointed out in the 60's in response to the article, blue color is not really a symptom. Peters seems to identify the 'bluish' reference as a plain misreading. Blood-red or 'bilious' (golden brown) colors would be more consistent, but Peters points out that many things can discolor urine, and criticizes them for ignoring all the cases where the urine was described as normal-looking.

Peters also points a lot to the difficulty of diagnosing porphyria on the basis of symptoms alone, and the rarity of the disease:

"The calculated probability that clinical symptoms will correctly identify porphyria is vanishingly small; indeed the probability of a false positive exceeds 99.999%. This is an expected consequence of a diagnostic test of imperfect specificity applied for a disease with a low prevalence. On statistical grounds alone, the case for the correct diagnosis of VP in the Royal Family is extraordinarily weak."

But on the other hand, Peters has supported his case with a machine-learning computational linguistics analysis - which is certainly a novel idea, but hardly a clinically approved method of diagnosis. He overstates his case, such as claiming that Macalpine's article was immediately dismissed by porphyry experts, in reference to among other critical letters by Dent (BMJ 1968, 'Royal malady'), but ignores the supportive ones in BMJ at the same time. Also neglected is the fact that Dent's first objection was that he did not believe porphyria was as serious a condition in the past, and that the more severe symptoms invariably "followed administration of modern drugs". A skepticism of drugs not untypical of the time, but the point on porphyria isn't held to be true today.

But the most significant problem I find with Peters articles is that he completely ignores and dismisses genetic evidence, which (I feel) ought to be highly significant when it comes to a rare genetic disorder. In their follow-up, Macalpine et al had found two living descendants of George II with the diagnosis. Less significantly, they felt they'd found evidence of the condition in ancestors of George and other members of the house of Hannover. Not long after that publication, Prince William of Gloucester, a living direct descendant of George III was diagnosed with variegate porphyria, independently by several doctors. This is almost entirely ignored by Peters, and dismissed in one instance with:

"The significance of any evidence about the descendants of George III depends in great measure upon the original assessment of the King’s symptoms. Quite simply, if George III did not have porphyria in the first place, then tracing the condition in descendants is irrelevant."

Dismissing possible evidence that your theory is wrong by the fact that it'd be irrelevant if the theory is right, is a bit disingenuous. Dishonest, even, considering that he'd made statistical arguments against the porphyria diagnosis. Knowing George's descendants and relatives have the diagnosis ought to make it much more likely that he may have had it. Inheritance patterns and thus the probability varies depending on the specific type of porphyria, but it certainly ought to be far higher than the "99.999% false-positive chance" of the Hift, Peters, Meissner paper would seem to indicate.

A weaker support of Macalpine's theory was indications of arsenic poisoning found in 2005 in hair samples. Arsenic binds chemically to the protein in hair, so it remains there for a long time even after the poisoning occurred, and lasts as long as the hair itself. The main problem problem with the analysis though, is that arsenic compounds have been used for conservation of things in the past, so it's not always possible to exclude the possibility of contamination. (although samples are washed before analysis to try to remove any surface arsenic) Anyway, the reason why this would be significant is that arsenic exacerbates the effects of porphyria. It may be hard to judge the relevance of it, though.

Personally I don't have an opinion. If it's not clear from the above, I think both Macalpine-Hunter and TJ Peters seem a bit guilty of overstating their cases and ignoring evidence against them. If it hadn't been for the genetic evidence I might've been on-board with Peters, as there's not much evidence in favor of of porphyria specifically, and it's a rare disorder. But when multiple living relatives have been confirmed to have it, the very rarity of the condition works in the opposite direction. It is a question that might be definitively answered if they ever get a DNA sample of George, or survey his descendants.