Is distributing copies of the Qur’an at cost considered an ongoing charity (Sadaqa Jariyah)? Does the distributor bear the sin for any typographical errors within them? And must he cease distributing them?

This act of selling copies of the Qur'an with a good intention is a good deed, but it is not considered an ongoing charity (sadaqah (definition) jariyah) because you are selling the Qur'an copies and not endowing them. As for the presence of a typographical error, it does not affect the permissibility and validity of the sale, and there is no sin upon you in that, as it is something difficult to guard against.