I'd be embarrassed
If this where the site of my organization, I'd be embarrassed if my (potential) clients saw this for minutes hours on end:
It always amazes me how organizations spend lots of money to polish their front door, but don't add a bit of monitoring to ensure the door doesn't squeak.
Of course a catch with Nagios is that people tend to monitor their systems from inside the same network. Meaning problems go unnoticed, and also outgoing alerts may never reach a destination at times when you most need it
In that case, 3rd party monitoring sounds like a better solution: http://www.watchmouse.com/
Quite right, though I prefer to set up my own external monitoring if at all possible.