Kerik didn't pay nanny taxes, and didn't validate the immigration status of his nanny. the "warrant for his arrest" relates to an appearance failure in a civil case regarding someone who did work on his house, for which payment was in dispute. and he had an issue with accepting a gift from a firm doing business with the city, a violation of the NYC charter.
And there were many other allegations, including the one working through the system now that he lied on his application.