So far as none trivial but solvable problems - there's going to have to be communication with all vendors operating delivery drones. Each drone will have to be aware of other drones by other companies and their flight-paths in the area and avoid collisions.
The biggest problem that I can see is the customer and public themselves. What is to stop someone stealing drones? Or plain vandalism of them? Follow it in a car to it's destination and you know it's going to have to come low enough down for a quick grab. Otherwise if there's some controlled drop off point, air rifles or crossbows or other publicly available small projectile weapons.