"Everything Randi talks about is perfectly true if you use the contemporary understanding of the word 'homeopathy'.
Which he wasn't. He was specifically talking about homeopathy in the period when it was invented and when it came to the US in the mid 19th century. In fact he even talks about 'the proving', which as a far as I know isn't even actively done anymore in modern homeopathy. (I'm pretty sure the modern manufacturers are just reusing old formulas and not actually doing new 'research'.)
He gave some historical background but also brought it around to how homeopathic preparations are presently made, with the examples of actual products using 30x and 1500x dilutions. There are lots of specifics we could be pedantic about, but I agree with the grandparent that for a 15 minute summary of homeopathy it's on target.