What are necessities when it comes to everyday bags? And what are common problems with handbags?

For me, the organization of the bag pockets/sections is definitely the biggest necessity/problem. I don't like too many sections or little pockets, but there should be some division within the bag. Also, whether the bag is carried by hand or on the shoulder matters a lot too. The bag shouldn't be sliding off my shoulder if it was meant to be worn on the shoulder, right?