If you just ignore the error message and start using the iPad, it will work...however......HDMI is a very flaky interface on any device. Different versions of HDMI abound, and they all don't play together very well
In order to get my iPad 2 to play on my TV using the adapter, I had to turn the TV off then back on in order for the video to show. I sometimes have to do that when I switch to my Time Warner cable box which is connected to the TV. Mst of the time it works, but sometimes either the audio or video won't work - the cable box is probably 5-6 yrs old, and it's HDMI is likely a different version than my TV- which is only two yrs old.
The Digital AV Adapter I have is brand new. Once I connected it to the iPad (while it was on and the TV was off), then turned th TV on, the iPad video was mirrored on the TV. Every app I've tried works and views OK except Amazon Instant Video (who now say their new app doesn't support viewing on an HDMI connected TV using an ad). I think they just screwed up the app - I can't believe they would design it that way.
I tried Safari, and a few games and they all view OK on the TV using the adapter. I haven't tried every app though.