Q:

What is the "Long-Wavelength Error" reported for SRTM data? 

Assessments of SRTM topographic products (like Rodríguez et al 2005 and 2006) report that height errors showed coherent long-wavelength signatures and describe long-Wavelength error characteristics.  
But although I have exhaustively sought what it exactly means I can't figure out to what "long-wavelength" refers to.  What is the long and short-wave components of SRTM errors? 

A:

In the article from 2006, linked in your question, there is a section named "SRTM Error Sources".  It goes into details on each of the three components. 
Based on that article, the following answers to your questions can be derived.   
Long-wave components of the SRTM errors 

An error in knowledge of the baseline roll angle will induce a
  cross-track slope error in the estimated topography whose magnitude is
  equal to the roll error.  The SRTM instrument used a sophisticated
  metrology system (AODA) coupled with post-flight filtering and
  estimation of the baseline position.  The main components of the
  baseline motion are due to the natural modes of oscillation of the
  mast.  These motions can be modeled and removed so that they do not
  constitute a dominant error source.  In addition, the baseline position
  is affected by the Shuttle’s attitude maneuvers.  The time scale for
  residual roll errors is long, resulting in spatial errors with
  wavelength on the order of thousands of kilometers.  They constitute
  the primary source for long-wavelength residual errors.  Rodriguez et
  al. ( 2005) show a representative example of this residual
  long-wavelength error estimated by subtracting the sea surface
  topography, which is known to centimetric accuracy from the SRTM
  estimated topography.  The peak values of this residual error are 10
  m.

As such, the long-wave component is from residual errors from the roll correction - meaning that it arises from movements of the shuttle. 
Short-wave components of the SRTM errors

These errors are due to two sources: random thermal or differential
  speckle noise and systematic phase changes due to antenna pattern
  mismatches or long term drift of the instrument electronics.  The noise
  contamination results in height errors which are random and which
  exhibit short spatial correlation lengths.  These errors cannot be
  compensated during ground processing.  The antenna patterns for each of
  the channels do not have identical far-field phase characteristics.  If
  uncompensated, this phase mismatch results in a net systematic phase
  error (called the phase screen) which is a function of the look angle. 
  Due to the stability of the antenna far-field phase, this phase screen
  can be estimated by binning the height errors over the ocean as a
  function of look angle and applying the mean phase bias as a function
  of angle as a phase correction to the interferogram.    To estimate
  this phase screen, SRTM collected data prior and after each
  continental crossing, as well as for a small number of basin-wide
  ocean data takes.  Estimates of the phase screen were obtained as a
  function of time and for each of the four SRTM elevation beams and all
  beam positions.  The phase screen correction was not observed to change
  significantly over the mission lifetime; the estimated changes in the
  height error correction were estimated to be below 10 cm. 
  Finally, a small slow drift of the differential phase was observed
  over the lifetime of the mission, probably due to slow changes in
  instrument temperature.  The residual phase errors induce cross-track
  tilts which are practically indistinguishable from the residual roll
  errors discussed above. 

With the above in mind, the short-wave component comes from two elements types of problems:
(1) short term sensor stuff, aka.  thermal noise in the sensor - differential speckle noise - systematic changes due to antenna pattern mismatch
(2) long term sensor stuff, aka.  drift of instrument electronics
As for the naming of the error types - the wavelength refers to the scale a which the error types are seen.  The "long-wave" components cover thousands of kilometers, while the "short-wave" are small scale random noise.