Their iniquity, i.e. the punishment due not only for their own, but also for the people's miscarriage, if it be committed through their connivance or negligence. And this was the reason why the priests withstood king Uzziah, when he would have burnt incense to the Lord, 2 Chronicles 26:17,18.
Related Commentaries of Numbers 18:23
Numbers 18:23
23 But the Levites shall do the service of the tabernacle of the congregation, and they shall bear their iniquity: it shall be a statute for ever throughout your generations, that among the children of Israel they have no inheritance.