This is amazing, and has the potential to be majorly disruptive. It has that golden thing that PayPal has—the ability to take payments from regular credit cards, without the other person needing to be a user of the service. Thus, it is immediately useful to merchants, and will spread from them to non-merchant users.
I wonder how they're going to deal with people recording credit card numbers off the website, e-mails or phone, then typing them into Square to charge the customers as if they were handed the real card. That's not allowed by the card brands, and it's Square that's at risk of being terminated if they let it happen.
Slick. Love it.
Though... call me paranoid, I wonder if anyones ever just taken off after having the vendor give them the iphone for signing/receipt.