There are no big problems... when the delivery is made on a lawn, like in that video, but if you have to make it to a tenant on the third floor, things are a little different.
Ever since drones were born I thought that a service of that kind wouldn't be possible here in Italy: some good person would steal the drone.
In other countries, where you can buy a gun in the fruit shop, like in the USA, they would enjoy "drone hunting".