Does the Apple TV 3rd gen support 1080p via Airplay

Welcome to the Apple community.

The new Apple TV supports 1080p basic airplay, providing that the original source video file is 1080p itself. Mirroring unfortunately is still 720p even on the new Apple TV.

Yes, it should, at least for the new iPad

• AirPlay Mirroring to Apple TV (2nd and 3rd generation) at 720p
• AirPlay video streaming to Apple TV (3rd generation) at up to 1080p and Apple TV (2nd generation) at up to 720p

http://www.apple.com/ipad/specs/

Nice, always first. I like you.

FWIW, it doesn't matter if the iPad is a first or second generation model, the criteria is whether the source video is 1080p or not for basic airplay.