This is an update to my earlier post. 

I had the same problem with my T-Mobile Galaxy Note 2 after updating from 4.1.2 to 4.3. I am using the Actiontec ScreenBeam Pro. Screen mirroring on my wife's T-Mobile Galaxy S3 was not affected by update.

I finally decided to bite the bullet and restore my phone to factory defaults. My screen mirroring now functions flawlessly again. Please note that I did NOT restore my phone from a backup for two reasons (phone contacts re-installed themselves):
-I did not want to re-install many of the apps anyway
-I did not want to take the risk that I might be putting the same problem back into the phone

I manually re-downloaded most of the apps that I wanted back onto the phone, re-configured my ring tones, home screens etc., and most of the other things that you have to do after restoring to factory defaults. Thus far, everything is working now (except that I missed two phone calls that did not come through, but I cannot duplicate the issue whenever I test it).

I also wanted to get my "Google Experience" launcher working again so that I can launch "Google Now" using only my voice, which is working again now as well.