First, you should definitely listen to the full interview because they go into depth on the internet's effect on how we read and then conceptualize the information to make associations. These are the underpinnings of our analytic capability, and Carr believes that on the whole we're losing a lot more of our associational capacity that we used to have when our brains weren't bombarded with interruptions. Our brains like to hoard data, and the way the internet works and (increasingly often) designed to provide lots of tidbits that excite us and alter our neuroplasticity. They do go into some counterarguments.
Also, an update to The Shallows has been re-released recently on the 10-year anniversary, which is why Ezra Klein interviewed Carr. Klein seems to have had a volte-face moment in which, as a blogger, he was dismissive of any critique about the internet because it was an instantaneous resource-rich environment. Now he understands that when he reads he's always searching for what he calls this "fugue-like" state of "deep reading" that allows him to understand and connect what he's reading to other arguments and topics.