Not all are compatible with the note 3. Seems to be a change introduced in android 4.2, but the kz500 mentioned in another post works fine with the 10.1 (and the original note) but does not work with the note 3.
I have a similar problem. Motorla kz500 v122 keyboard. It will pair but then fail to work as a keyboard with my Note 3.
After pairing on the note 3, input changes to the extent that screen based input no longer works with swipe, but their is no response to any input on the kz500. Note 3 is...