If your MDI window is open / visible, then you may have a communication status icon - it will be green when everything is in order, orange for warnings (for example, damaged packets are detected, but comms is still working, and the system has recovered), and red - for errors (for example, without decoded messages received within 5 seconds). This allows you to make it pretty subtle when everything happens, but the "other" is pretty noticeable - the problem.
For a serious error (for example, a shutdown), you may want to get more “invasive” because there comes a point when the problem with attracting user attention is no worse than worrying about them with an error message.
If your window is not guaranteed to be visible, then (despite your dislike of the idea) the system tray icon (to show this status) is a standard and fairly clean solution - it can be constantly visible or just appear when it relates to it as non-invasive, because you can still get the information into the user’s attention, and it’s easy for the user to check periodically to convince himself that they have a green light.
An alternative to visual indicators is the use of sound signals.
(For example, we use a monitor on our assembly server. It simply has a green icon when the assemblies are good, and a red icon if the assembly failed. This is fine, because it does not bother me all, but I can check the status of the assembly in an instant.
Alternative example: I have an email application that displays the envelope icon in the system tray when I have a new letter, and nothing if I do not. In practice, with this system, I notice quite soon (in a minute or two) when the mail arrived, but I do not care about the constant pop-ups or message boxes.
I think these are both examples that show how much better the icon in the system tray is than a popup or a ball window. Pop-ups are annoying, and most of them, if you don’t watch when they appear, you skip the information. I will always see pop-ups the same way they disappear, and then I need to open the application to see if they tell me anything useful. This is usually not the case. The same goes for sound notifications: I continue to hear random noises from my IM application and wonder what they mean).