If the mistake happened in the typesetting stage, printed books could spread errors much more efficiently, as in the infamous "wicked bible" of 1631, where a typesetting error made the ten commandments contain the amusing phrase "Thou shalt commit adultery". Surviving copies are quite the collectors' item as most were destroyed.

https://en.wikipedia.org/wiki/Wicked_Bible

Usually, though, errors are corrected and every every printing has fewer errors than the previous one.

What percentage of books get a second print run on a printing press? And what's the process for that? Do they have to reset each word for the second run? I genuinely don't know how a physical process like typesetting can result in increased accuracy on each print.

Any interesting book gets a second print run - except if it was on purpose a limited edition with some exceptional quirk.