That would be covered by the reader threshold. Mom-and-pop sites are not normally going to get high volumes. If something happens to "go viral", then you'd be obligated to inspect it. Maybe an exception can be given if such spikes are rare. But if your site *regularly* has content that has say 50k+ views a month, then you should know to keep an eye out.
As far as doxxing, if somebody points out an unwanted address or phone number, the mom-and-pop can just take it down, as there shouldn't be any such thing in there to begin with. Except maybe for businesses: If it's a business contact directory, that's a bit more complicated, but generally would be considered a commercial endeavor, not citizen expression, and commercial endeavors are generally more heavily regulated.