This is what I just posted for someone else as I fixed the issue without Affecting my security, but at a price:
So I have a mid 2013 MacBook Air and when I upgraded to Mavericks the airplay mirroring stopped working. I tried many fixes from the forum and none helped. I called phone support and they said to restart and hold down Command + R and select reinstall Mavericks, which installs the OS all over again, but, doesnt lose any settings or files. I tried this and reset all of my hardware and readded all of my accounts to my Airport Extreme and my 3rd iteration Apple TV. None of this helped.
I then downloaded an installation of Mavericks 9.2 and found a program to make an install disk on a thumb drive. I backed up all of my files in my docs and my music to a removable disk and made sure that I had most of my small stuff in the iCloud. I erased my MacBook HDD and installed a fresh (full) install and not an upgrade (from Mountain Lion). This worked like a champ.
I will note that Im a Network Admin and have tried three different firewalls in Mavericks and this probably screwed up my communication with my Apple TV. I could still, however, use iTunes and my movies and music on the TV, but could not mirror from my desktop. After the fresh install, I notice that my Air is speedy quick and seems to run better than it EVER ran, even after I installed all of my fancy security stuff as well. As with MOST operating systems, a clean install is ALWAYS better than an upgrade, DUH. The p[roblem COULD have been the upgrade, OR the settings left over by all of the uninstalled software I had tried out. I will never know for sure, But, I will go back to my previous statement about the effectiveness of a fresh installation.
SO, i downloaded a full install of Mavericks 9.2 and used diskmaker X and restarted holding down the option key and deleted my previous install and then selected the USB drive (8GB) with the autoinstall I made. Worked like a charm and reloaded all of my stuff back. Would like to also point out that my Chromecast device also started working again from the computer as well. I hope some part of this brain dump helps you folks, as it was a real drain on my time doing so much troubleshooting for naught.