The correlator is interesting. I don't see how it works. In the perfectly-tuned case, how does delaying the signal by half an (IF?) period and inverting it yield a match for the original signal? Inversion isn't the same as a delay.

I guess the idea is that the 70 kHz IF is effectively sampled at 2x the necessary Nyquist cutoff needed for 15 kHz baseband audio. So the signal content at half the period can be relied upon to match after an inversion and delay, assuming it was (a) band-limited at the source (or by the clever deviation-reduction scheme), which it would be; and (b) tuned correctly.

The application note gives more details [1], but I find it a bit confusing. The idea is that as long as you are within about +/- 100 kHz of the station (a wide range), the radio will lock onto the right frequency (because of the frequency-locked loop), giving the nominally 70 kHz IF. Since the 70 kHz signal doesn't vary much over a half-wavelength (as you said), the correlator will be happy. The correlator will still stay locked as the IF varies +/- 15 kHz with the audio signal. (The correlator doesn't require a perfect match, just mostly matching.)

The problem is that if you mis-tune the radio by 100 kHz or so, the FM detector will give you an output, but it will be distorted. The issue is that the FM detector is linear over a small range, but outside that range, you get non-linear side lobes. So if you tune to a side-lobe frequency, the radio will lock onto the frequency, but the output will have harmonic distortion. In this case, the IF frequency is way off from 70 kHz, enough that the delayed signal and the inverted signal don't match at all, so the correlation fails and mutes the audio. Then you'd re-tune and find the right frequency.

[1] See Figures 8-12. Link: https://www.tel.uva.es/personales/tri/radio_TDA7000.pdf