Halion said:
So to get back on my question, does a low z source, like a mic, connected to a hi z input, like a guitar amp, cause any problems impendance wise? I'm purely asking this as a technical and not a practical question, I know the sound will probably suck in this example.
Well, as you pointed out, there's balanced/unbalanced and there's low/hi Z. Yes, they are separate issues, but quite often they are linked, as in your example. You wouldn't be able to plug a a low Z mic into a guitar amp, since a low Z mic runs on a balanced (3 conductor) line and the high Z guitar amp input is unbalanced (2 conductor).
Distortion, if what it is that you are talking about ("sounds terrible" is pretty general) is most commonly generated from one gain stage overdriving the next one, i.e., clipping. In a signal chain from mic to speaker, there are several gain stages, and if any one of them is overdriven, there's garbage from there on; there's no way to "unclip" a waveform by running a later gain stage cooler.
When you set trim pots on a PA to balance the gain, you are effectively compensating for any impedance mismatches you may have at that point. Your prob could have been something as simple as the trim pots being set too hot on the input channels of the PA. That wouldn't be an impedance prob per se, though impedance is part of the equation.
You may be looking for a rule like "you can't plug a low Z signal into a high Z input", but it's not that simple. What you really should be looking at is balancing gain stages.