What is iTunes Error 13019?
The Apple Support Page for this error (now a broken link), "iTunes: Error 13019 during sync," gives quite a few solutions. The first one is to make sure you're on the most recent version of iTunes (which you stated that you are). On that page, you'll notice that there are some drop-down arrows that reveal more suggestions. The second one tells you to disable Voice Memo syncing. There are some more helpful procedures there if the voice memos aren't the issue.


  Resolution
  
  Update to the latest version of iTunes. The latest version of iTunes can be downloaded from this page. If updating to latest version of iTunes does not resolve the issue, continue:
  
  
  Error occurs while syncing music
  
  The error will most commonly occur while syncing music. This issue can be resolved by following these steps:
  
  
  Select the device name in iTunes under Devices.
  Click the Music tab and under the Sync music option, choose Selected playlists.
  Deselect the Voice Memos playlist.
  Click Apply and then click Sync.
  
  
  If the above steps do not resolve the issue, check the device and the iTunes library for duplicate voice memos. If you find any duplicate voice memos, delete the duplicates and then sync.
  
  If those steps do not resolve the issue, then follow these steps:
  
  
  Select the device name in iTunes under Devices.
  Click the Music tab and deselect the Sync Music option.
  Click Apply and then click Sync.
  After the sync is complete, reselect the Sync Music option.
  Click Apply and then click Sync.
  
  Test in a new user account
  
  If the steps above do not resolve the issue, attempt to sync with iTunes while logged in as a new admin user. Follow these steps to create a new administrator user:
  
  
  Windows XP, Windows Vista, and Windows 7
  
  
  From the Start menu, choose Control Panel.
  Open User Accounts.
  Select Create a new account and follow the instructions to complete the account setup 4. process.
  Once the new account is created, choose Log Off from the Start menu.
  Log in to the newly created user account.
  
  Mac OS X
  
  
  From the Apple menu, choose System Preferences.
  Choose View > Accounts.
  Click the "+" (you may need to authenticate to be able to click this).
  Give the new user account a name and short name and enter a password.
  Select the checkbox for "Allow user to administer this computer". This makes the user an admin user.
  Click Create Account.
  Log out and then log in to the new account.
  
  
  
  If the error does not occur in the new user account, other content is causing the error. Proceed to the next section.
  
  If the error does occur in the new user account, the issue may be caused by content downloaded or created on the device, such as podcasts and voice memos. Removing content from the device may address the issue.
  Error occurs while syncing other content
  
  If the error occurs while syncing content other than music (applications, podcasts, and so on), perform the same steps as above, but deselect the content that stops the sync. Deselect one type of content, then attempt to sync. Continue until you sync without error. Deselect Apps last, since restoring your Apps would take longer than restoring other content.
  


Source: http://​support.apple.com/kb/TS2830