AirPlay Mirroring is a highly bandwidth intensive, low latency technology. All of our previous wireless APs (access points) were wireless N specification and yet the AirPlay Mirroring experience with a class full of students was unreliable. Increasing the number of APs to balance wireless usage helped, but not to the standard we were after.
After investigating various wireless vendors we made the move to Aerohive APs. It has greatly improved our AirPlay Mirroring experience and has allowed us to reduce our total number of APs. Now, each classroom containing an Apple TV also has an Aerohive AP330.
Special attention is required when positioning APs; for example, mounting an AP to a celling containing an air-conditioning duct may dramatically reduce the APs SNR (signal-to-noise ratio) and greatly impacts throughput. WiFi Explorer is a Mac application for tracking signal to noise ratio of APs. A good AirPlay Mirroring experience requires a SNR of at least 25dB.