Old buildings and old infrastructure, from the days when lead pipes and lead paint were the norm.

Lead remediation costs money, and landlords aren't super interested in taking care of the issue. They just paint over the peeling walls and leave it to the renter not to eat the paint and get their own filtration systems. (Note that Brita filters do not remove lead.)

As for rats, we're in a city with lots of places for them to live. Although Providence instituted standardized garbage toters over a decade ago, that doesn't stop folks from feeding wildlife, having stacks of wood for their fireplaces, and doing other otherwise benign things that make the city appealing for them. Holes in old foundations make easy entries into buildings.