updated 11:15 pm EST, Thu February 27, 2014
Issue does not affect all users; differing types of failures reported
Threads in the Apple Support Communities reporting issues with AirPlay mirroring and extended displays after installing OS X 10.9.2 have appeared, with no clear pattern or cause determined as of yet (though having older hardware may be a factor). Apple released 10.9.2 on Monday to address a serious SSL vulnerability and to upgrade some features. Users have reported a menagerie of different issues, complicating the situation.
AirPlay glitch as discovered by AppleInsider
According to AppleInsider, reported problems range from AirPlay mirroring disappearing as an option, to audio-only connections on Apple TV, to an inability to mirror or extend desktops to another display using AirPlay. Both AI and MacNN have run tests on OS X 10.9.2 on a variety of hardware, with differing results.
AI was able to recreate some issues with a mid-2011 MacBook Air and third-generation Apple TV (running 10.9.2 and iOS 6.0.2, both the latest releases for those devices). It also tested a late-2013 MacBook Pro with the same model of Apple TV, but in that case no issues were reported. MacNN tested a 2009 MacBook Pro and performed AirPlay audio and video tests with an iPhone 5s and a third-generation iPad (the former on 10.9.2, the latter devices on iOS 7.0.6) with no issues.
That said, most of the users reporting the issues had previously (under 10.9.1 or earlier) used AirPlay without issue, indicating a genuine problem, but the social comparing of notes on the problems has only recently begun and thus far haven't found a common identifier. The issues were said to persist through hard resets and other troubleshooting.