MOTM

The example with the 7.5k sine wave is a good one but the analysis 
is faulty.  It doesn't matter what the waveform looks like after 
conversion to digital.  What matters is that the harmonics which are 
present in the digital representation of the waveform which are not 
present in the original sine wave are all higher than one half the 
sample rate and will therefore (in theory) be removed by the filter 
in the D to A converter.  In practice, as has been stated here is 
that the filters are not perfect and neither is the clock.  The lack 
of perfection in the filter and clock are what causes the harshness 
in digital sound.  Filters and clocks are much better than they used 
to be and in high quality pro gear can be outstanding.  Many lower 
quality and lower cost converters sound bad becasue of the poor 
quality of the filter and clock.

As far as the problem being in the mixing not in the conversion:  
This can be true, it depends on the internal bit depth of the 
software/hardware combination that makes up your mixer.  If you have 
only 24 bits internally and first reduce the level of your signal by 
48 db and then reamplify it by the same amount you are left with a 
16 bit signal rather than a 24 bit one.  The system I use (ProTools) 
has an internal bit depth of 56 bits which is more than sufficient 
for extensive processing without fidelity loss.  I assume most pro 
grade systems are similar in bit depth.  The quality of the 
processing algorithms are very important as well.

The Nyquist criterion is provable mathematically assuming perfect 
filters and clocks.