Geojarv - I'm having the same problems getting iPad 2 output via HDMI to the TV.
I have an iPad2 using Apple's 30 pin to AV Adapter. I originally thought this was an Apple not supporting Samsung thing so I tried it on the Sony Bravia TV downstairs with the same results.
I've tried plugging in both the Apple 30 pin connector and HDMI cable thinking it might need power but that didn't help.
I get the TV icon in the Video playbar letting me toggle output choices. Sometimes it says Dock Connector or not at all (just showing Airport Extreme Audio or Apple TV). On my iPhone 4 playing Video it will toggle between Dock Connector and iPhone in the output options.
Using a $24 Central Computer iPhone/iPad to HDMI knock off connector I have gotten this to work in the past, but because I ran into issues I went and picked up the official Apple AV Adapter cable. Currently neither solution works so I'm wondering if this is an Apple iOS (6.0.1) issue since I've swapped out the other variables (2 TVs, 2 iOS devices, 2 HDMI cables, 2 HDMI adapters).
I'll keep playing with it, but I'm not currently able to help my kid with his school video project because I can't figure a clean way of screen recording from his iPad into iMovie.
thoughts?