Considering that a major factor behind Japan's surrender was the Soviet invasion of Manchuria, which began on the same day as the bombing of Nagasaki, the idea that "the war was already over" seems a bit out of touch.

It's true that a misinterpreted signal has not led to retaliation... so far. We've been quite lucky. If Vasili Arkhipov had been a little more cranky on October 27, he could easily have been convinced to agree to launching a nuclear torpedo at American forces. Similar with Stanislav Petrov in 1983, although it's an open question as to how the leadership would have reacted had he informed them of the supposed attack. In 1995, Russia came within two minutes of deciding to "retaliate" in response to a scientific rocket launched from Norway. A slightly different trajectory or radar reading could easily have made the difference there.

Given the past 71 years, the risk of accidental nuclear war appears to be fairly low. However, we have no real idea if "fairly low" means the risk is 1% per year or 0.000001% per year. Both are consistent with what we've seen, but the former means that nuclear war is extremely likely in the medium term, while the latter means we can probably ignore it.