The stability of the individual elements of a two-dimensional (2D) regular array of single domain particles is investigated. The variance in the statistical distribution of up- and down switching fields of the elements leads to premature switching for the low coercivity particles, and incomplete overwriting for the high end of the distribution. The distribution of the interaction fields from surrounding elements on a 2D array depends the saturation magnetization of the elements, their packing density, and the recorded information. The non-ellipsoidal shape of the elements leads to reduced switching fields as a result of non-collinear magnetization around the corners and edges. The thermal stability of 2D arrays, switching by (incoherent) rotation of the magnetization, is enhanced compared to bulk/contiguous media, due to the lack of low energy barrier domain wall motion processes. However due to the fast decrease of the anisotropy, stability at elevated temperatures is still a problem. Experimental data for a model 2D square array of single crystalline, strongly uniaxial, single domain garnet particles illustrate the effects on stability of statistics, shape, and thermal excitation.