I'm going to hold further judgment on the paperless system. I suppose the chance of errors is minimized when the waiter/clerk/bartender scans your card immediately instead of walking off with it such as on the pool deck when you order a drink. I think most errors happen when a bartender has several orders and the wrong cards are scanned. I've also seen them type in a folio number on the screen, instead of scanning the card. That is an error-likely situation.
You are supposed to be able to pull up all your purchases on your cabin TV for review, and they are supposed to be immediately viewable.