A theoretical and experimental analysis of the growth dynamics of colloidal crystal films deposited by evaporation induced self-assembly is herein presented. We derive an expression for the film growth velocity from which we obtain an equation that describes the evolution of the forming crystal thickness with time. Its validity is confirmed by comparison to the experimental profiles of a large number of films grown under different conditions. We find that, on top of the already reported linear increase in film width over long distances in the growth direction, periodic variations of the friction force at the meniscus give rise to short-range thickness fluctuations that are the main source of spatial inhomogeneities observed in these lattices. The key parameters that determine the period and the intensity of these fluctuations are identified.