What's the distance between the center of mass and geometrical center of Earth (CM-CF offset)?
There is no inconsistency between the 2012 paper and the older reference(s).

Fig. 2 arbitrarily sets all the components (x,y,z) of all the displacement vectors of all the centers to zero at the beginning of the time period (about 123,000 years ago).  

Furthermore the 2012 article states:


  The horizontal movement of
  topography associated with plate motion will then change the CF.
  Over time, these slow phenomena can create large offsets, up to
  hundreds of meters, between CM and CF. When the evolution of
  the internal load is reasonably inferred from other sources, then
  these processes may be able to explain a significant bulk of the current
  static offset between CM and CF.


Planetary Sciences, table 1.2, says the distance between CF and CM is 0.80 km, citing to Yoder 1995.  

See also Evidence for convection in planetary interiors from first-order topography The Moon March 1973, Volume 7, pages 172-180


  It has been known for some time
  that a center of mass-center of figure offset exists for the Earth (e.g. Jeffreys, 1962).
  From a spherical harmonic analysis of the Earth's topography with the oceans replaced
  by an equivalent mass of rock, Balmino et al. (1972) find the center of mass
  displaced by 1.1 km from the center of figure in the direction 145°W long and 42 ° S lat.


And from the NASA memorandum Reports of planetary geology program - 1981:


  For Earth, with its combination of sialic ([denisty]~2.7) and simatic ([density] 3.0-3.3) crusts, the CF is displaced toward 41.6°N, 34.7°E, in the direction of the Eurasian shield, and close to the center of the continental province at 46°N and 27°E (Bills and Ferrari, 1978). 


See also Geocenter - Degree 1 :


  The spherical harmonic coefficients of degree 1 represent the distance between the center of mass of the Earth and its 'center of figure', which in practice is the center of a set of tracking stations on the surface of the Earth. Because of their physical meaning, time changes in degree 1 coefficients can be expressed in several equivalent forms (1) as distances in mm along the Z (along the axis of rotation), X and Y axes; (2) as (fully normalized) coefficients of the geopotential; (3) as the changes in mass (per unit area) that would give rise to the geopotential coefficients, expressed either in kg/m^2 or cm of equivalent water thickness.  The relation between these forms can be found in Swenson et al (2008), equations 5 and 4...


And Planetary Surface Processes (2011):


  In fact, the Earth itself has a substantial center of mass – center of figure offset if the water filling the ocean basins is neglected. The floor of the Pacific Ocean is about 5 km below sea level, whereas the opposite hemisphere is dominated by the continental ... The waterless Earth's center of figure is thus offset from its center of mass by about 2.5 km at the present time.