Does the iPad 2 HDMI out adapter work with the new iPad?
Based on comments on the new adapter on Apple's online store, the iPad 2 HDMI adapter is not fully supported with the new iPad:

Is this a new HDMI AV Adapter ?
It is exactly a new product with the compatibility for the new iPad.
If you try to use the previous adapter on the new iPad it will tell you &quot;This accessory is not supported&quot;

My guess is that the new screen resolution of the new iPad has led to this incompatibility. Besides, with the old adapter the best you could get was 720p, with the new one it's boosted to 1080p.