In Brave New World (1980), the titular society relies heavily on computerized systems for their world to function. For the most part, these systems work perfectly as intended and do not fail. The only computer failures in the movie are both due to human error.
The event that kickstarts the entire plot of the movie is due to human error of a contraceptive device. Women in this society are put into two different buckets, those with uteruses and those without (the freemartins). The women who still have their uterus all wear these small circular devices on their belts. These devices are controlled much like a rotary phone and must be programmed by the person who wears it to prevent pregnancy (24:45). When Linda Lysenko goes on vacation with Thomas Grambell to the savage reservation, she doesn't use the device properly and ends up pregnant. I imagine if this happened while Linda was at home that there is a protocol to deal with a pregnancy, but at the savage reservation where she ended up after being abandoned, the only protocol is to simply give birth. This causes the creation of John and kickstarts the predicament that Bernard Marx and Lenina Disney go through due to finding him at the reservation. Overall, failure to use the contraceptive device properly is likely not the worst deal in the world, unless you're Linda of course, and you can ultimately only cause damage to yourself, which is not the case in my next example.
In the brave new world, children are not born naturally, and are instead grown in plastic bags. A part of this process is the initial embryos going down a conveyor belt where operators add fluids and minerals to their petri dishes. Certain castes of civilian in this film have additives added, like alcohol, that stunt their growth, development, or cognitive abilities. One of the main characters, Bernard Marx, is an Alpha Plus, one of the highest castes, but their was an issue during his development that made him shorter and have a different mental process than his fellow Alphas. This is because while his embryo was on the belt, the technician was distracted and accidentally added some alcohol to him. This completely changed the the course of his life, as he was often picked on for being weird and not having the same affinities as everyone else. It's likely that Bernard is not the only person this has ever happened to, as Lenina is shown later in the movie causing an error, with her coworker saying that it isn't a big deal due to the embryos she affecting being of a lower caste. These machines do inform the user if there is an error, with a large warning sign and an audio cue, but it's clear that the operators don't fully comprehend that they're affecting peoples lives. These operators are all Betas, so it's likely they might not be able to fully understand this due to effects put on them before birth.