These are purely assumptions based on what I saw on the video alone:
>If my friend and I walk out side by side, how does it know (if it does) which items are mine and which are hers?
Looks like the entry/exit is the same type of set-up you find at most large office buildings with the tap in/out gates (see screenshot: http://i.imgur.com/e7fDglY.jpg). I assume it only lets one person out at a time which also suggests your friend could only enter the store if they had an amazon go account and tapped in themselves.
>What happens when someone picks up an item and leaves without first doing whatever check-in/registration/setup is necessary?
Again, based on those gates, I'd assume you can't actually access the store without going through the necessary set-up first.
Personally, I'd like to know what happens if/when my phone battery dies in-store.