Suppose that you have a simple, benign solution that works only up to Y% optimization (just make the paperclips), and a hard, non-benign solution that is optimal above that point (take over the world, then make paperclips). The AI naively follows the benign strategy, and does not look too hard for alternatives up to Y%. All manual checks below Y% of optimization pass. But Y ends up as a number that falls between two of your numerical checkpoints. So, you observe all checkpoints passing below Y% optimization, until suddenly the AI switches to the non-benign solution between checkpoints, executes it to reach the next checkpoint, but has already caused damage.