I opened a case with Apple Tech prior to Thanksgiving about this issue and another issue. I noted that not only could I not log into iTunes and was receiving a FATAL error message (This was an Apple issue and has since been remedied by Apple.), I also mentioned the problem I was having syncing my podcasts and new music purchases, and listening to podcasts via the Podcasts app on my iPhone 5S running the new OS. When the Applecare Tech responded, she addressed the podcast issue. Although some of the things she recommended I have already tried, but I'll pass them along just in case someone else may want to give them a try. Note that I did do every single one today and will see if the problem persists. I too find myself needing to make sure the "Use Cellular Data For" in the iTunes Store is selected, along with checking "Manually manage music and videos" in Summary for my iPhone. Applecare's response:
As a suggestion, kindly download the latest version of iTunes. It can be downloaded free of charge at the Apple website:
http://www.apple.com/itunes/download/
Mac users will also need to install the latest version of QuickTime:
http://www.apple.com/quicktime/download
If you have an iPod with video, be sure to update it using iTunes after upgrading to the latest version of iTunes.
If you are able to update to latest version of iTunes but problem persist kindly try the steps below.
One thing to keep in mind, due to the overwhelming response to the new iOS 7 and iTunes 11.1 updates, there is a higher then usual volume of traffic. Downloading, connecting and updating may be slower and you may encounter temporary issues with accessing the iTunes Store.
Please try the following trouble shooting:
Please sign out of the iTunes Store. Open Settings > Store > Scroll down and Tap the ID > tap Sign out.
Then Clear cookies on the iOS device:
1) Quit App Store or iTunes in multi-tasking.
2) Tap Settings.
3) Tap Safari.
4) Be sure cookies are not set to "Never"
5) Tap Clear History.
5) Tap the Clear History button.
6) Tap Clear Cookies and Data.
7) Tap the Clear Cookies and Data button.
From computer:
1) Open iTunes
2) At the top menu, click File > Preferences (iTunes > Preferences on a Mac)
3) In the Preference menu, click the Advanced tab
4) In the Advanced menu, you should see a button that says "Reset Cache". Please click this button.
It is critical that your date, time, and time zone be correct:
1. From the home screen, tap Settings > General > Date & Time.
2. If the option exists, turn off Set Automatically.
3. Verify the time zone and time (in the status bar) are correct for where you are currently.
4. If not, adjust the incorrect setting accordingly.
5. If everything was correct and the option exists, turn on Set Automatically.
Next, please hard boot the device. This will purge the device of the actions it is doing. For example, it would purge any stalled downloads. To hard boot an iOS device, you will want to hold the home button and the power button at the same time until the device powers off.