An entire system can go down because a single bit which should have the value 0 has the value 1, or vice-versa.
However, everyone has problems with details to some extent. Otherwise, we wouldn't have software defects. A reasonable software development process does not rely on hiring perfect people who take care of every detail and never make a mistake. (By saying which I don't intend to blur the distinction between missing a detail, or getting a details wrong.)
Alan Perlis once wrote the following epigram, #32 out of many:
"Programmers are not to be measured by their ingenuity and their logic but by the completeness of their case analysis."
That's the important thing: getting all the cases right and not missing any.