Part of the utopian idea of Star Trek: Into Darkness is the fact that computers and computer systems are essentially flawless, with the exception of interference (e.g. hacking). Chapter 8 spends a lot of time talking about the societal issues that stem from computer errors. Between innocents being arrested and missile systems malfunctioning, there is a wide range of consequences. In Star Trek, they never have the problem of the computer malfunctioning. The only computer system problems which arise in Into Darkness come from Admiral Marcus sabotaging the Enterprise’s warp drive. If nothing had been tampered with, there would have been no issue with the ship’s computer. Following the idea of a computer working until it is tampered with, the crew of the Enterprise find themselves with limited resources after being bombarded with torpedo hits and other shots from the enemy ship. If they had not been repeatedly shot, their systems would still have been fully functional.
The closest thing to a “computer issue” found in Into Darkness is not literal, but an analogous situation when Khan beams the photon torpedoes over to his own ship. He threatens Spock that the torpedoes had better be what he was expecting, to which Spock replies “Vulcans do not lie.” Of course, Spock being half human, he has indeed deceived Khan. Since Vulcans operate solely on logic, much like a computer, they do not lie (just like computers). However, this “computer” has a “bug” which makes it unreliable.