In the US, IIRC they have a trusted person sort the bills by denomination for them -- like a friend or a bank teller -- and then they fold them into different orientations so they know what they've handed to a checkout clerk. No way for them to prevent being shortchanged, unfortunately.

I guess technology could help though - this would be a great application for smart glasses.

Some countries chose different physical sizes and/or embosed bumps in the corners.

I really don't know. Even as a seeing person you need to have your wits about you, and I think most people sort notes by value in their wallet. Most other countries have notes whose size and color differs by value, so it's much harder to make mistakes.