Hello, as the resident Taiping specialist here it seems if you were expecting anyone in particular, it'd be me, so my thoughts, first general, then specific:
Overall I thought it was reasonable as a discussion of Hong Xiuquan and his early leadership of the kingdom, but less so one of the Taiping Heavenly Kingdom as a whole. If you wanted to, you could shift the anniversary under discussion back one day to 20 March, for the capture of Nanjing by the Taiping in 1853, and make the podcast be about the lead-up to that, instead of implying further discussion without going into it. There's the odd error of fact, but a lot of it is very understandable. So a good start, but would need a little tweaking.
As for the specifics:
At around 2:25 you mention that 1837 was the third time Hong attempted the exams. This is true, but the following segment about his receiving the Christian tracts from Edwin Stevens belongs to his second attempt, probably in 1836.
As for Edwin Stevens, he's the most likely possible candidate but we don't know for absolute certain – neither Hong nor his associates ever identified the missionary in question as Stevens, and Stevens, who died in 1837, left no written recollection of the event, if it ever even was significant enough for him to do so. Jian Youwen in the 1950s argued the case for it being Stevens on the basis of elimination, having argued that Hong Xiuquan's second exam attempt was in 1836 – if Hong's second exam was in fact earlier, then it need not have been Stevens. All this to say that there should be a 'probably' there.
You were rather brief on the visions themselves, which in my view anyway is reasonable – there's a lot of embellishment in the more detailed accounts produced by the Taiping. I would note, though, that it would be worth adding in a couple of dates just to make things clear – if Hong indeed became interested in the Christian literature of his own accord (which Theodore Hamberg's account, probably the most reliable, suggests otherwise), he did so in 1843, some six years down the line, in the wake of a fourth exam failure.
Separately, referring to the celestial/Heavenly father as 'God the Father' would be a bit misleading – the Taiping conception of divinity was basically unitarian.
As for the Taiping version of the Bible, it's not impossible that Hong Xiuquan was working on it as early as 1847, but from what I've gathered, particularly in Jonathan Spence's book, serious edits to the Bible, outside a bit of censorship to the end of Genesis 20, began only after summer 1855.
At around 5:15 you go into the currents of discontent Hong was tapping into, which is always good. It'd be worth noting a few things, though. Firstly, the impact of the loss in the Opium War is often overstated: there was some economic impact to be sure, but it's not clear that Qing prestige was particularly damaged. Secondly, Hong's initial exposure to Christianity predated the Opium War, and although his time with Roberts took place after 1842, Roberts had been in China since 1837.
You also skip round with time a bit – the Heavenly Kingdom was founded at Jintian in 1851, and did not finally relocate its capital to Nanjing until March 1853. Also, skipping to 1864 is a bit quick – I don't know how much you feel you'd like to fit in there, but it feels we've had the start and end but not the middle. Separately, 'Third Battle of Nanjing' seems to be a Wikipedian invention or similar.
Good mention of Mao-era admiration of Hong, but as far as I can tell, the idea that Hong Xiuquan has been compared to Li Hongzhi (the Falun Gong founder) by Chinese academics has no real basis in fact. The book Wikipedia cites for the claim discusses speculations by Western academics on possible reasons for CCP opposition to the Falun Gong, and what seems to be non-academic opinion on the topic, rather than a survey of Chinese academia on the matter. The modern opinion seems to be more ambivalent than anything else.
Pronunciation isn't a huge issue in the grand scheme of things, but just as a handy guide:
Hong Xiuquan – you've got the 'Hong' pretty close, it basically sounds like 'hung' in a Northern English accent. For 'Xiuquan', that involves a lot of sounds not commonly found in English – the best readable approximation would be to use the Wade-Giles, 'Hsiu-Ch'üan'. To offer the best approximation I can, it's something like 'See-oh' but as one syllable, followed by 'tsuen'.
Guangzhou – almost there the first time round, though the 'zhou' portion should be pronounced basically just like the name 'Joe'.
Hangzhou – as above.
Qing – often pronounced 'ching', technically closer to 'tseeng'.
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