Since kitkat 4.4.2 was released on the Galaxy Note 3, many users were unable to write files to the External SD Card. Below is a simple fix for rooted users on the Galaxy Note 3 N9005 ( International Snapdragon Variant).
**Please be advised that I have only tested this on my personal N9005. However, you are free to test it on your own devices at your own risk!! **
1. Using a root-enabled file manager, navigate to /system/etc/permissions
2. Edit platform.xml and find the WRITE_EXTERNAL_STORAGE permission.
3. Add an additional group definition for this permission...<group gid="media_rw" />
4. Save the changes to the file.
Attached is a copy of my platform.xml.