As almost always happens, the new models that appear on the market either from one company or another usually suffer certain setbacks that are improved in successive batches. This is why Apple has already warned in a support document that the last Macs released at the end of 2013, may present connectivity problems when the 'Mirroring' function is being performed, using the Airplay protocol when the Wi-Fi network is old or slow.
To fix this issue, Apple strongly recommends that we turn off the Bluetooth connection to improve the audio and video streaming transmitted by Airplay, since otherwise there could be episodes of cuts or freezes in the image and sound.
Specifically we can read at the entrance,
Airplay freezes or drops connections than on a Wi-Fi 802.11 b / g network
Symptom
When using a MacBook Pro (Late 2013) or Mac Pro (Late 2013) with AirPlay Mirroring on an 802.11 bog network, the TV picture might freeze or the connection dropped.
Decision
Disabling the Bluetooth connection can improve Airplay performance considerably. To disable this Bluetooth connection, look for the Bluetooth icon in the bar menu in the upper right corner of the screen. Click on the icon and select 'Disable Bluetooth'.
We can see that this occurs only in Wi-Fi networks that do not support the Wi-Fi n standard, of which really at the domestic level there are not too many, since even 100% of the operators already offer free modems-routers with this capacity or even any modern neutral router also incorporates this feature.
Even so, if you notice any kind of problem in this regard and you don't have an excessive distance between your devices, you can try turn off Bluetooth.
More information - What to do if your Mac doesn't use the maximum WiFi speed
