What's the impact of aliasing in the time domain?
I read Footnote 8, 


  "The complication is that because of the sampling, the total system
  is not time-translation invariant and so does not have a unique
  ‘impulse response’ – the response is slightly different according to
  the position of an original impulse relative to the sampling points."


as a cumbersome way of saying that aliasing corrputs an LTI system such that its response can no longer be trusted to be linear and time-invariant. 

If I were to rephrase things informally, I'd say that:

When a signal is undersampled in the frequency domain or has inadequate frequency resolution (aka freq domain aliasing), its spectrum has overlapping tails. 



That means that it is no longer possible to correctly reconstruct the time-domain signal. The spectrum tails do not go to zero, but are folded back. This inversion of the tails are what we know as aliasing and manifest themselves in the time-domain signal as impulse responses (a short-duration time-domain signal) that mix with the original signal. 

These mixtures are perceived as distortion/roughness/etc. Their constructive/destructive effect give you your "quasi-random" amplitude modulations.

The magnitude &amp; position of aliasing in the time domain is related to the degree of frequency domain undersampling. See https://ccrma.stanford.edu/~jos/sasp/Example_2_Time_Domain.html



Finally, regarding "time smearing", the impulsive (quickly rising) parts of a waveform contain many high-frequency harmonics that when undersampled in the frequency domain, fold back as described above. However, I wouldn't call this distortion smearing, in the transient-smearing, or pre-ringing sense.

Hope that helps!