Context. Dust grain dynamics in molecular clouds is regulated by its interplay with supersonic turbulent gas motions. The conditions under which interstellar dust grains decouple from the dynamics of gas in molecular clouds remain poorly constrained. Aims. We first aim to investigate the critical dust grain size for dynamical decoupling, using both analytical predictions and numerical experiments. Second, we aim to set the range of validity of two fundamentally different numerical implementations for the evolution of dust and gas mixtures in turbulent molecular clouds. Methods. We carried out a suite of numerical experiments using two different schemes to integrate the dust grain equation of motion within the same framework. First, we used a monofluid formalism (or often referred to as single fluid) in the terminal velocity approximation. This scheme follows the evolution of the barycentre of mass between the gas and the dust on a Eulerian grid. Second, we used a two-fluid scheme, in which the dust dynamics is handled with Lagrangian super-particles, and the gas dynamics on a Eulerian grid. Results. The monofluid results are in good agreement with the theoretical critical size for decoupling. We report dust dynamics decoupling for Stokes number St > 0.1, that is, dust grains of s > 4 μm in size. We find that the terminal velocity approximation is well suited for grain sizes of 10 μm in molecular clouds, in particular in the densest regions. However, the maximum dust enrichment measured in the low-density material - where St > 1 - is questionable. In the Lagrangian dust experiments, we show that the results are affected by the numerics for all dust grain sizes. At St ≪ 1, the dust dynamics is largely affected by artificial trapping in the high-density regions, leading to spurious variations of the dust concentration. At St > 1 , the maximum dust enrichment is regulated by the grid resolution used for the gas dynamics. Conclusions. Dust enrichment of submicron dust grains is unlikely to occur in the densest parts of molecular clouds. Two fluid implementations using a mixture of Eulerian and Lagrangian descriptions for the dust and gas mixture dynamics lead to spurious dust concentration variations in the strongly and weakly coupled regimes. Conversely, the monofluid implementation using the terminalvelocity approximation does not accurately capture dust dynamics in the low-density regions, that is, where St > 1 . The results of previous similar numerical work should therefore be revisited with respect to the limitations we highlight in this study.