Inside the United Nations General Assembly this week, world leaders tackled the gravest issues facing humankind. Nuclear weapons. Tensions in the Persian Gulf. Fears of a climate apocalypse.

Outside, Stu Sleppin was carrying around a blue plastic dog-poop bag for almost half an hour because security teams had whisked away all the garbage cans in his neighborhood. Alongside Mr. Sleppin was his rhinestone-collared Havanese, Zoe.

“Police...