We've not been able to duplicate the problem on any of our devices, but after helping several people, we have come across what looks to be a working Touch ID fix for those affected. Best of all, it's a simple one!

How to fix Touch ID not working in iOS 8.3

Launch Settings on your iPhone or iPad Tap on Touch ID & Passcode Enter your Passcode or Password Toggle iTunes & App Store to OFF Press the Home button to return to the Home screen. Reboot your iPhone or iPad. (Here's how) Enter your Passcode or Password at the Lock screen Launch Settings on your iPhone or iPad Tap on Touch ID & Passcode Enter your Passcode or Password Toggle iTunes & App Store to ON

That should fix any issues with using Touch ID to authorize App Store or iTunes Store purchases.

For in-app use, remember you may have to enter a password in the specific app before Touch ID will work again in an extension (because your iPhone or iPad rebooted during update). For example, you'll have to launch the 1Password app and enter your Master Password at least once before the 1Password action extension will work with Touch ID in other apps.

With any luck, that'll get Touch ID working again for you in iTunes and App Store, and you'll be happily authorizing away! If you're having the problem, let me know if this fixed you up!