If the information from Gizmodo's sources is correct, the upcoming Xbox 360 Elite console will only feature HDMI 1.2 instead of the 1.3 standard.
This basically means the Xbox 360 Elite may not be able to play the newest lossless Dolby Digital+ nor True HD audio formats.
The current Xbox 360 units will also get a Spring update:
Answering other questions, both Xbox 360 Elite and current Xbox 360 units will have a spring (console) update which adds support for different video levels for VGA output (“7.5 IRE vs 0”). And as someone mentioned, using this setting you should be able to use computer monitors in addition to TVs with resolutions all the way up to 1080p with high fidelity and no issues with HDCP handshaking. So for current users, I highly recommend trying this update with your VGA connection to see if it does the job for you. Note that this is a console update and will work for both games and of course, HD DVD. The HD DVD software update is separate from this (and will be available on both Xbox Live and xbox.com).