While there is no direct example of computing reliability in Inception, the entire movie provides many allegories to the idea. The concept of dreams having levels in the movie is very similar to how computer architecture is set up, but instead of dream levels, it's something like hardware, the OS, or a piece of software. In the movie, if one level of the dream collapses, then the entire dream collapses. In real life if a piece of hardware or the OS is missing, then the computer will, most often, be rendered useless.
One very important aspect of computer reliability is redundancy and having backups. The characters in the movie use something called a 'kick', something that allows them to wake up and get out of a dream. In computing, people use things like a UPS(Uninterruptible Power Supply) or server backups in order to protect their computing systems against failures. While they may not serve the same metaphorical function as the kick, they do have the same purpose, to provide a backup plan when things go wrong. In Inception, if someone was to die in a dream while under sedation, they run the risk of getting trapped in something called limbo, a place said to be made up of decaying memories. Getting trapped in limbo could be seen as something closer to a total system failure, which would be the worst possible outcome from a reliability standpoint.
All in all, the dream realm depicted in the film shares a great deal of similarities to the digital world we know today. While Inception is science fiction, the struggles and challenges relating to the dream world mirror those faced by computing systems and networks today. In both scenarios, maintaining stability and safety is key.