If your MDI window is open/visible, then you could have a comms status icon on it - this would be green when everything is fine, orange for warnings (like corrupt packets have been detected, but comms is still working and the system has recovered), and red for errors (like no decodable comms received for 5 seconds). This allows it to be fairly subtle when things are wokrking, but quite noticeably "different" is a problem occurs.
For a serious error (e.g. disconnection) you may want to get more "invasive" because there comes a point where not bringing the problem to the user's attention is worse than bothering them with the error report.
If your window is not guaranteed to be visible then (despite your dislike of the idea) a system-tray icon (to show this status) is a standard and rather clean solution - it can be permanently visible or simply appear when it is relevant, it's about as non-invasive as you can get while still bringing information to the user's attention, and easy for the user to check periodically to reassure themselves that they have a "green light".
An alternative to visual indicators is to use audio alarms.
(For example, we use a monitor on our build server. It simply has a green icon when the builds are good, and a red icon if a build has failed. This is perfect, as it doens't bother me at all but I can check the build status in an instant.
Alternative example: I have an email app that shows an "envelope" icon in the system tray when I have new email, and nothing if I don't. In practice with this system I notice pretty soon (within a minute or two) when mail has arrived, but I am not bothered by constant popups or message boxes.
I think these are both examples that show how much better a system tray icon is than a popup or balloon window. Popups are irritating and with most of them if you aren't watching when they appear, you miss the information. I'm forever spotting popups just as they disappear and then having to open the app to find out if they were telling me anything useful. Which usually they weren't. The same goes for audio notifications: I keep hearing random noises from my IM application and wonder what the heck they mean).