Are any first or third party HDMI adapters out, or at least have a real release date yet? That was the biggest hesitancy I had when I bought the tab yesterday, so I'm curious.
No news yet, however there is a video of someone using the Galaxy Tab (7") dock with the mini HDMI port along with the 10.1 showing full mirroring.
I've done this successfully as well. I took the 7" dock and a 10" dock and swapped the bracket. I can now drop in the 10.1 into the dock with the mini-HDMI connector attached to my TV and pretty much everything works.
When non-video is active the screen is mirrored to the display. If you run the tablet in portrait mode the image on the TV is sideways.
When an app runs video the video on the tablet is "missing" but shows up full screen on the TV. The HDMI output will automatically switch to match the resolution of the streamed video. I've seen it work at 720p and 480p. I haven't actually witnessed 1080p yet though.