Thank you for your suggestion. We hope to include this when the next improved version of Live Chess comes out.
ECO codes for observation
If we had ECO codes on games in progress, giving the opening/variation the observation function could become a study tool. So what do we have to do to make that happen?

The functionality is already there on online chess and that makes sense. Live games however...would you have that resource/time to refer to lines when playing over the board? I believe the spirit of the 'live' version of chess on this site is to play the game with the normal constraints of over the board chess as opposed to correspondence chess. As far as studying games is concerned, you can always analyze your own games later.
Would it be possible to put the ECO codes next to current games so as to give the chess.com'er a way to find relevent lines to observe? Such as lines they would normally play?
thank you