Please can you clarify exactly what you mean by linear and non-linear imperfections in analog and digital systems, for both myself and others reading this.
Linear means the change is the same regardless of signal level. Non-linear means the change depends in some way upon the signal level.
A good example of linear would be a simple volume change: if you turn down all your faders by 3dB you get exactly the same result as if you turn down the masters by 3dB and (ignoring the slight difference in headroom and noisefloor in the analog version) this holds true for analog and digital mixing. Likewise, an EQ can be thought of as a frequency specific volume control, so if you notch out 3dB at 3KHz on every single channel, you get the same results as if you notched out that frequency on the master instead.
A compressor is linear so long as the ratio is 1:1 (hence the straight diagonal line you see in the transfer graph of some plug-ins) but as soon as you wind the ratio up you introduce a non-linearity, and the results start to depend on the incoming signal level. Inserting a comp on every channel is obviously NOT the same as inserting a comp on the master, even with identical settings. The same applies to distortion; loud signals are affected much more than quiet signals, and because the artifacts are level-dependent we also get inter-modulation effects when distorting the whole mix that would not have been present when distorting individual channels. Again: equally valid for analog and digital systems.
Of course, an analog EQ will have a much smaller linear range than a digital EQ. Part of the craft of analog mixing is to set your gain staging to stay within the linear range of the equipment. Perhaps the artistic side comes in when you begin to deliberately exploit the non-linearities at the extremes; that's not something I can do with gain staging ITB, but I could load a saturation plug instead...
re: +/- 3dB swings and nature of imperfections: surely a 3dB variance per channel across 16 channels equates to a 3x16dB variance total, or some equivalent, summed, across the mean?
They are all running in parallel, so they won't accumulate as you imply: that would require you to patch the output of each channel into the input of the next so one signal passed through all channels in series. To return to the volume example: if you turn 48 individual channels down by 3dB you get the same result as turning the masters down by 3dB. 48 * 3 dB = way too much!