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Recent approaches to demonstrating adaptive optics and atmospheric turbulence have made use of spatial light modulators (SLMs) as the active phase element. However, there are limitations in using SLMs as an accurate method of simulating turbulence phase screens. In this work we investigate the limitation of laser beam shaping with a phase-only spatial light modulator for the simulation of dynamic and pseudo-random turbulence in the laboratory. We find that there are regimes where there are not sufficient pixels to resolve the phase. At the higher end of this range, at strong turbulence levels, the zonal regions are tightly packed. This leads to two simultaneous effects: a phase screen with low efficiency in some regions, and a modified turbulence structure due to the shifting of the zone peaks. These amplitude and phase distortions have a deleterious effect on the accurate simulation of the turbulence. At the lower end of the range, at weak turbulence, the phase change is too small to describe with sufficient grey scale levels, since the full 256 levels are associated with a full 2π phase shift. Further limitations include the frame rate of SLM for time-evolving turbulence. We show experimental results demonstrating these limitations, and discuss the impact this has on simulating turbulence with SLMs.