  We further characterize the structures tentatively identified on thermal and
chemical grounds as the sites of dissipation of turbulence in molecular clouds
(Papers I and II). Our study is based on two-point statistics of line centroid
velocities (CV), computed from three large 12CO maps of two fields. Probability
density functions (PDF) of the CO line centroid velocity increments (CVI) over
lags varying by an order of magnitude and structure functions of the line CV,
up to the 6th order, are computed. We show that the line CV bear the three
signatures of intermittency in a turbulent velocity field: (1) the non-Gaussian
tails in the CVI PDF grow as the lag decreases, (2) the departure from
Kolmogorov scaling of the high-order structure functions is more pronounced in
the more turbulent field, (3) the positions contributing to the CVI PDF tails
delineate narrow filamentary structures (thickness ~ 0.02 pc), uncorrelated to
dense gas structures and spatially coherent with thicker ones (~0.18 pc)
observed on larger scales. The confrontation with theoretical predictions leads
us to identify these small-scale filamentary structures with extrema of
velocity-shears associated with gas warmer than the bulk. Last, their average
direction is parallel (or close) to that of the local magnetic field
projection. Turbulence in these translucent fields exhibits the statistical and
structural signatures of small-scale and inertial-range intermittency. The more
turbulent field on the 30 pc-scale is also the more intermittent on small
scales. The small-scale intermittent structures coincide with those formerly
identified as sites of enhanced dissipation. They are organized into
parsec-scale coherent structures, coupling a broad range of scales.
