A recent Apple knowledge base article on the subject of the iTunes 13001 error explains a few steps you can take to resolve the issue.
- Sometimes the issue in syncing can be related to one type of content. Try syncing one thing at a time (e.g., just photos or just music). If the error occurs after syncing a particular type of content, replace the offending files with backups or new copies.
- If you experience the sync problem while syncing photos, try syncing from a different folder, like your Desktop folder.
- If the sync problem exists with iTunes content, try rebuilding your iTunes library. If it only occurs while syncing with iPhoto, try rebuilding your iPhoto library (hold option + command while clicking to open iPhoto).
- If all your content seems to cause the issue, try creating a new user account. Open System Preferences, click Accounts, and click the (+) button to add a new account. Be sure to give the account Admin privileges. If creating a new user resolves the issue, compare your processes using Activity Monitor to determine if a background process is causing an issue with syncing. Quit that process in your original account and attempt to sync. If you continue to have issues syncing, you may want to try and sync your iPod Touch or iPhone with a different machine. If you are able to sync, further troubleshooting steps on your Mac may be necessary. Consider reinstalling a fresh download of iTunes from apple.com or reinstalling the latest Combo Updater for your version of Mac OS X.