I just answered specifically to the comment, referring to the security aspect. Paypal was losing 10 million USD from fraud, so hope won't do it for the security.
"assume that people aren't going to be swiping their cards with random people"
Assuming, just won't do it.
I'll also mention that folks swipe their cards in fake ATM swipers pretty regularly. It hasn't hurt ATM usage, in general. Likewise, PayPal fraud is still an issue that they fight every day...but PayPal is incredibly profitable. eBay and craigslist also have huge fraud problems, but again, the sheer volume of legitimate transactions and the value of the huge markets they serve is enough to overcome any misgivings people have about using the services. So, I don't think that fake swipers will make this particularly company any more or less trusted than existing providers that have to fight fraud (assuming they are vigilant about actually fighting it).
The interesting thing here is that PayPal made all their margins by encouraging people to use bank accounts rather than credit cards because they made almost no profit on credit card transactions. I'm interested in how this revenue model will work out, it seems like merchant services providers have arrived at their current model of business (arduous checks before granting accounts) out of necessity. Since Square is basically in the merchant accounts business (that's where their margin is) it will be interesting to see if they actually know something that merchant service providers do not about granting accounts to anyone who wants them without more verification.
I've always wondered why merchant service providers didn't instantly verify accounts and allow people to start charging immediately, but hold the captured funds while the account was verified with all the proper checks. Maybe that is what Square is doing.