Distortion in amps;most/least annoying?

As nothing is perfect,which forms of distortion in amps,or
which anomalies can you live with? And what sorts do you find annoying, to the extent of taking away the pleasure, from listening to the music.
The worse and most annoying i have ever had in an amp is static through speakers. Its happening right now and its really p*ssing me off as i cannot get it out of my head, even when the music is playing. That small background noise you just know is there somewhere is just sooooo annoying.
To broaden the response a bit, I find the distortions in electronics much more irritating than the distortions in transducers, i.e. speakers and phono cartridges. It seems that the distortions in electronics are less consonant with the struture of the music. That said, solid state type distortions that start to pile up in the upper midrange/lower treble drive me nuts. As hunter/gatherers this may be the range that we are most sensitive to.
Right now I'm looking to add sone second order distortion to the upper mids. Might bias the drivers hotter. Intrestingly my speakers (Omega) are wired with bigger gage on the positive than the negitave. I wonder?
Any kind of coloration. Enhanced mids, rolled-off highs....
I don't need the the amps to interpret, filter or exaggerate , just amplify as honestly and competently as possible. It's not always pretty and it's easy to be tricked by a convincing liar.