The experience I see thus far for AirPlay with 3rd party apps, on both iPhone and iPad, is that only the audio is output to the AppleTV but not the video. This is great for Pandora but not so good for any video app. Is this a bug with AirPlay or do the developers need to update their apps to support it properly?
According to John Gruber, this is not possible, unfortunately:
AirPlay is the killer feature for Apple TV. But perhaps we’d better keep that in the future tense for now: it’s going to be the killer feature for Apple TV. After installing today’s various software updates for iOS devices, the only apps I’ve seen where AirPlay works for video are the built-in iPod app (a.k.a. “Video” on the iPad and iPod Touch) and YouTube. In other apps, AirPlay is audio-only.
You'll note right up top that it's now totally possible for 3rd-party apps to spit video over AirPlay (as of iOS 4.3; been this way for some time now.).
Jobs stated in an email it will be available in 2011:
Q: [...] I just purchased Apple TV and was wondering are you ever going to make airplay video work for videos in safari and 3rd party apps? [...]
A: Yep, hope to add these features to Airplay in 2011.