How do the authors represent the role of the “human factor” within the rationalized and “mechanized or technologized” system?

The overall perspective on the human factor is concerned with duty. While the key characters have little opportunity to interpret possibly erroneous information, they must act based on their understanding of their duty, which includes allegiance to their civilian or military position. The primary representation of the human factor is through the character of the US president. Although technically a civilian is most regards, the president is the Commander in Chief so ultimate military authority resides in him. As such, he must make the difficult decisions to send the Skyscraper fighters after the Vindicator bombers, and then to negotiate with the Soviet premier. The other important character in this scenario is Colonel Cascio; his sense of duty combined with mistrust of the Soviets lead him to open rebellion. In terms of implementing the plans, both Colonel Grady, the leader of the attack squadron, and General Black, who must ultimately carry out the New York attack, exemplify true allegiance to their position and their country.

Fail-Safe is a nuclear-age parable of man's imperfection and self-destructiveness. The authors depict a scenario in which the military has supposedly created, with the computer technology then (in 1962) available, a "fool-proof" mechanism for defense against foreign attack. This also would prevent the launching of accidental attacks from our side. The theme of the novel is not so much the imperfection of the machine as it is the weaknesses and flaws of the human beings who have created it.
At the time Fail-Safe was written, the average person knew virtually nothing about computers and tended to think of them as awe-inspiring creations, incapable of error. A computer program, of course, is only as "perfect" as the person who designs it, and no amount of testing will uncover all the problems that can and usually will occur in real-time. The bug that makes it appear as though a Soviet attack is occurring could, perhaps, be rectified if the men then on their mission to oppose that attack were "perfect" themselves, or if they had some way of understanding that the efforts to recall them, to stop the plane from bombing Moscow, were genuine instead of the bogus messages they believe them to be. The attempts by the Americans to shoot down their own bomber before it reaches the target are doomed to fail; it has again been human error not to realize that the pursuing planes, though faster than the bomber, are still not fast enough to catch up to it and destroy it.
General Black, the man assigned by the president to bomb New York City in order to prove to the Russians that our attack is unintentional, has a dream vision in the opening pages of the book of a bullfight in which he cannot see the matador's face. The matador, of course, is General Black himself. The nightmare paints man as a killer who does not recongize himself as one until it is too late. The authors are perhaps saying that so long as man creates the machinery of death, he will end up using it, despite all the checks and balances he thinks he's employing.