I am pretty sure you are talking about lag created by your TV. The lag doesn't have anything to do with the 360. HDTV's generally have a 'game mode' option in their setup now. The picture quality goes down a bit, but it removes the lag created by the processing time of the TV.
Edit: I had to use game mode when I was playing Zack and Wiki. I was having the hardest time with the music box challenges until I remembered the HDTV creates lag and I turned on game mode. Guitar Hero is able to be calibrated to compensate for lag created by HDTVs.
Tag: Hawk - Reluctant Dark Messiah (provided by fkusumot)