Today I switched my Google account over to two-step verification and proceeded to go about resetting all my Google stuff with application-specific passwords (btw you don't realize how much you rely on Google until you have to go and re-enter passwords for everything lol). The GMail app alerted me that it couldn't connect as I expected and I of course gave it its new app-specific password which made it happy. I also set up the Google Authenticator app successfully. The only deal is no other app including the Market or the phone itself have asked for the new account details even after rebooting. I can download/update apps from the Market with no problem so I'm not really sure that I should be concerned at all. I was just expecting all of these apps needing new codes again and since I didn't get it I'm puzzled.