So far, the discussion has been about watching off-ball or mechanics, etc. Here's one other way to watch the game. I did this once and it's not easy. If you want to work on your "game awareness", then go to a game with a pad and paper.
Register the time on the game clock and shot clock after every whistle. Track the team fouls. Track the possession arrow. Record the number of every FT shooter. Log every player that subs out of the game; when the clock starts properly, cross out the numbers of the players who subbed out.
It's tough to do, but those are all things that we're supposed to know in a game anyway. It's easier to work on it while you're in the stands.