Apple Acknowledges Airplay Mirroring Issues for Late 2013 MacBook and Mac Pro on Slower Wi-Fi Networks
The company suggests that users who are experiencing issues with dropped connections and frozen images on the television when using Airplay mirroring should turn off Bluetooth.
Turning off Bluetooth can enhance the performance of Airplay considerably. To turn off Bluetooth, locate the Bluetooth icon in the menu bar on the upper-right corner of your screen. Click the icon and choose Turn Bluetooth Off.While it is unclear how widespread the Airplay mirroring issue is, there have been complaints about Airplay performance with the newly released MacBook Pros on both our forums and the Apple Support Communities. Users have noted both image freezing and significant lag when attempting to use Airplay mirroring.
Complaints about Airplay picked up in November, shortly after the October release of the latest Retina MacBook Pro models. Though there have been few complaints about the Mac Pro due to its limited availability, it is also displaying the same problem.
Because the issue is limited to b or g networks, another fix could include a router replacement supporting the n or ac standards.