Ok, this is for sys admin and paranoid people.
If you want see system logging in real time on your desktop there exist an amazing app: Xlog
Here you can see a beautifull screen on how it looks like:
Sadly, Xlog is no longer available in the App Store and stopped working since Mac OS El Capitan.
NOTE: you can set Xlog preferences to start it automatically on login. 😉
NOTE2: you can choose text & background color and transparency.