A couple of things (beyond “neat video”):
He doesn’t answer the question about what would happen if you left the light on. You might think this is no big deal, because he correctly says that the light dies out quickly. If you were in a mirrored room such that the average photon trip was 3m (and somehow not interact with you at all), and the mirrors are 99.99% reflective, a photon would reflect 10^8 times a second (i.e. once every 10 nanoseconds), but only reflect 10,000 times on average, so you would expect the room to go dark in less than a millisecond. However, if you keep the light on, you get a build-up of photons for that time. To reach equilibrium, your production rate and loss rate have to be equal, and you only lose 0.01%, or 0.0001 of your photons. If you have just a 1 Watt source of visible light (which would emit around 10^18 photons a second), you need to have 10,000 times as many photons inside to have 1 Watt leaking out.
Put another way, your source is emitting 10^10 photons per bounce interval (10 nanoseconds) but only 10^6 photons leak out. In the next interval, another 10^10 photons are added and 1,000,010 photons leak out (0.0001 from each generation). And so on, with a decaying exponential buildup, until you have 10^14 photons hitting at each bounce, so that 10^10 can escape. That’s when you reach equilibrium.
So your little 1 Watt light gives you a power buildup and you are doing the equivalent of hugging 10 kW of space heaters. Actually the scenario is worse, because your body emits around 100 Watts, in the infrared, so if the mirrors reflected IR you would cook yourself to death. Fast.
The other issue I have is where he says that mirrors flip left and right and not top to bottom. The initial explanation is right — they flip perpendicular to the plane of the mirror, but then he claims that L-R is perpendicular while U-D is parallel, which is nonsense. It’s a plane, so they are both parallel. Mirrors flip front-to-back, i.e. perpendicular. The confusion is that the mental image we have is of someone walking around the mirror to the other side, and that’s not what is going on. It’s a confusion of inversion and rotation, which are two different ways of getting an image like that. There is no left-right flip! Your right hand is still on your right, it’s just that you expect it to be on your left, because of that were a person in the mirror (who has rotated on an axis to look like that), it would be their left hand.
Maybe you’ll like hearing Feynman explain it.