Diffuse scattering in BaZnF4 is investigated by an x-ray method in the temperature range 410 10 K. Rodlike diffuse intensities are observed at room temperature. They indicate the occurrence of some (2a,2c) ordering in the (a,c) planes which are the planes of linked ZnF6 octahedra. Complete disorder takes place from plane to plane along the b direction. Based on x-ray and Raman data an interpretation of the diffuse streaks by two-dimensional dynamical clusters is given. It corresponds to a slow dynamics (<10 cm-1). It is shown that these clusters can be viewed as precursors of an instability of the same type as the instability giving rise to the incommensurate phase in BaMnF4.