  Lagrangian reconstruction of large-scale peculiar velocity fields can be
strongly affected by observational biases. We develop a thorough analysis of
these systematic effects by relying on specially selected mock catalogues. For
the purpose of this paper, we use the MAK reconstruction method, although any
other Lagrangian reconstruction method should be sensitive to the same
problems. We extensively study the uncertainty in the mass-to-light assignment
due to luminosity incompleteness, and the poorly-determined relation between
mass and luminosity. The impact of redshift distortion corrections is analyzed
in the context of MAK and we check the importance of edge and finite-volume
effects on the reconstructed velocities. Using three mock catalogues with
different average densities, we also study the effect of cosmic variance. In
particular, one of them presents the same global features as found in
observational catalogues that extend to 80 Mpc/h scales. We give recipes,
checked using the aforementioned mock catalogues, to handle these particular
observational effects, after having introduced them into the mock catalogues so
as to quantitatively mimic the most densely sampled currently available galaxy
catalogue of the nearby universe. Once biases have been taken care of, the
typical resulting error in reconstructed velocities is typically about a
quarter of the overall velocity dispersion, and without significant bias. We
finally model our reconstruction errors to propose an improved Bayesian
approach to measure Omega_m in an unbiased way by comparing the reconstructed
velocities to the measured ones in distance space, even though they may be
plagued by large errors. We show that, in the context of observational data, a
nearly unbiased estimator of Omega_m may be built using MAK reconstruction.
