After you start Console.app, just do "Hide Console.app" from app menu. When an event occurs, Console.app appears automatically and stays for two seconds to allow you to read what happened, then re-hides automatically.
You can change how long the windows remain on-screen in the Console.app preferences screen.
[Editor's note: I just noticed that Quake3 writes the game logs to the console.log file ... I'm not sure if that's a bug or a feature! ;-)]

