Does the video only consider sampling and reconstruction from the samples, or does he talk about quantization noise?

That I can perfectly reconstruct a band limited signal from samples taken above the nyquist limit is basic signal math. But any ADC is limited to a finite bit depth and this does introduce errors.

Not a signals guy, but I guess this is what the bandwidth theorem is about (snr vs signal power ratio or something).

Anyway, Im sure 16bit from my CD is perfect enough for anyone's ears and (obviously?) better than vinyl or cassette. But dammit I like analog music for the same reason I like my mechanical watch - I can really understand the full stack wholly.