I think this film is very useful. Would be good if it were shown in Russia with a professional translation (like they do it with Hollywood movies) on some of open channels (BBC is always part of a paid package). Though it is not worth a dime/penny from a military standpoint, IMHO it is not the main message to take into account and give a careful thought.
IMHO, it shows how fragile and imperfect is the current world order we are living with. Indeed, a group of 7-8 wise and knowledgeable people are forced (by the situation) to make strategic decisions nearly in real time, sitting somewhere in an isolated room and being fed by the info/data from other people with their interpretation. Technically speaking, the chain is error prone at each step. No matter how wise are you, you cannot make a dozen of right decisions in a row. And any error could be fatal. The "other" (read Russian) side is not shown, but it is obvious that in a similar room somewhere in Moscow the situation would be even worse because all those present there would be from the same camp, just listening to the chief guy (in UK there are at least are 2 competing parties). US is somewhere in between, IMHO (at least as it was with JFK during the Cuban crisis).
With all that said, IMHO the film clearly shows (though it is hidden behind the scene) that diplomats and politicians in the modern world are not doing their jobs well enough, while "the stakes we are gambling are frighteningly high".
Again referring to technical systems, there should be an "early detection" capability for any potential problem and effective mechanisms working 24/7 not to allow the situation to quickly advance to the critical line when some mad guys "on top of the hill" could either give an order to press the red (nuke) button or even let it be pressed without an order. E.g., we see it now how quickly the level of tension zoomed between Russia and Turkey (a UK "brother-in-NATO"). One more aircraft is down and hell knows where all this would go in one night.
Ideally, there should be calm, open and not time pressing/constrained discussions about real red lines giving certain respect to "holy cows" at each side, including informal ones. If the western leaders know (and they should know) that the issue of Russian-speaking minorities in the neighbouring countries is quite painful and very important to the Kremlin, why not to order their new vassals to behave accordingly? It costs nothing.... Instead, they close their eyes and allow ultra-nationalists do what they want.