From the shoppers' perspective, that single login is not that exciting, as most have been doing a very insecure replacement: using the same login/password for those dozens of sites. In effect, that's what PayPal is doing. The security impact is that if there is a breach—at PayPal, at that shopper's computer, elsewhere—that password can now be used to access all of those sites. At least that's the hole until PayPal is contacted and the password is shut down or changed.
In effect, PayPal is taking that very insecure consumer tendency—single credentials for multiple sites—and formalizing it under PayPal. Granted, PayPal's internal security is robust and well-thought-out, so from that sense, it's certainly a large security improvement for those shoppers. But if there is a breach somewhere—and it could just as easily be a Trojan that finds its way onto the shopper's phone or laptop, which bypasses all of the PayPal security—then the problem is the same. The thief can access every site that accepts PayPal. Put another way, it's perfectly secure until it isn't. And then it's really not secure.
Of greater potential benefit, though, is PayPal's mobile component. There are a very large number of low-cost programs today that will autopopulate user information (address, name, payment details, etc.) for desktops and laptops. But very few such programs today exist for mobile. PayPal's ability to fill out the mobile forms may make a huge difference in purchase completion.
Although mobile devices are used extensively for shopping and searching, most of those transactions stop when the item is placed in a shopping cart. That transaction is often completed later on a laptop/desktop. Even Macy's CFO has found those lower mobile conversion rates. That's because typing so much information into such a small screen is unpleasant, and doing so in a public area (think subway, plane, waiting room) can be awkward. PayPal's mobile autopopulate function could make a meaningful difference with mobile checkout.
On the down side, there's data control. This will deliver to PayPal a huge amount of data, data that PayPal has said before it will share with retailers. That's great news if that means sharing with your team. That's horrible news if it means sharing with your rivals. The reality is that it means both.