It's a shame that even though he had his hands on a very clean example with the facelift headlights and taillights that he didn't dedicate a few minutes to talk about them.
Easily the most iconic exterior design "quirk" of the E39 facelift was that it introduced the iconic halo 'Corona Rings' (i.e., angel eyes) as a modern interpretation of the quad-headlamps of prior generation BMWs dating back to the Neue Klasse.
Of course, this was later adopted en masse corporate-wide during the so-called 'Bangle-era' BMWs before transitioning to LEDs and adopting boxy, angular shapes that we're familiar with today.
Secondly, almost as iconic were the horizontal LED light bars that inspired an entire decade (and some) of BMW taillight design after the end of production of the E39 until their gradual abandonment with advent of the current 3D design.