Not one: several mistakes, or several failures, or several people in a submarine. Those systems all have multiple stages that require several validation steps to work, we do that for way less sensitive processes.
Nonetheless, yes, we're still on the brink of something gloomy. The movie is quite good, and would massively gain from spinoffs showing what happens in realtime in other countries too.
Also: how confident are we in the safeguards that, say, North Korea or Pakistan have in place? And how confident are we in the systems that tell us, and our adversaries, that an attack is taking place?
“His subsequent decision to disobey orders, against Soviet military protocol, is credited with having prevented an erroneous retaliatory nuclear attack on the United States and its NATO allies that would have likely resulted in a large-scale nuclear war.”
Nonetheless, yes, we're still on the brink of something gloomy. The movie is quite good, and would massively gain from spinoffs showing what happens in realtime in other countries too.