Here's another good one:
We fell through the ice when we tried not to slip
I can give you countless examples of people who proceeded very cautiously, trying to avoid minor mistakes, only to fail because they didn't notice a much bigger problem.
I develop, write, and validate analytical methods that are used by quality control analysts for drug release. These methods must be flawless. A mistake could lead to countless patients getting an incorrect dose of a drug, or a toxic impurity could end up in an entire batch. Because these procedures are so important, each one is peer reviewed, Quality Assurance reviewed, and the receiving lab also peer reviews and QA reviews the procedure. A second analyst also executes the procedure and looks for any errors and comments on any points that need clarification.
By nature, I am a very thorough person. I rarely make mistakes. People get used to that, which is actually a bad thing because I do make occasional mistakes. People who review my papers tend to look for minor "slips". For example, I got back review comments recently, an it was marked up for minor formatting errors such as a mis-aligned indents, page break in a bad place, grammar wasn't exactly right, etc.
After going through the hands of 8 people who are trained specifically to look for mistakes, not a single one of them noticed that the title of the procedure was for the wrong drug substance!