Money must flow from a source to potentially multiple destination. Because of that previous fact, you must have at least two postings per transaction (the double in double entry). If you manage to move money correctly without any errors, those postings in that transaction will add up to zero, making it trivial to verify you've done everything correctly without any errors.
> can't two errors cancel each other out and you still wind up at zero?
They can, but the probability of two opposite errors of exactly the same magnitude is much lower than of any individual random error.
It's the same as with any other error-correction encoding. You don't have a guarantee that all errors will be caught by it, but most of them can be, so it's useful overall.
