The Android 4.4 KitKat brought some useful features to the already feature-packed software on the Galaxy Note 3, but it also introduced an issue that disabled compatibility with third-party accessories. Samsung acknowledged this issue and said it would release an update to fix it, and that update has finally begun rolling out, with Poland being the first country to get it. The update also fixes the issue of apps not being able to write to the external storage on KitKat, and is currently available for the quad-core variant (SM-N9005) of the Galaxy Note 3.
It's good to Samsung acting so fast on fixing a rather glaring issue that should never have existed in the first place, though hopefully it will be as quick at actually making the update available in more regions (and for the Exynos model.) The update's currently available in Russia and Poland with build number N9005XXUENB3, and you can head over to the Settings » General » About device » Software update menu to do a manual check if you're too impatient about waiting for the update's notification to pop up on its own.
Update: The SD card writing issue, as it turns out, isn't related to Samsung's version of KitKat, but is caused by changes made in Android 4.4 by Google. Developers must update their apps to make them capable of writing to the external storage again, so if you use an app that isn't able to access the microSD card on KitKat, you might want to ask the developer to update that particular app.
Thanks, Ken!