New results are reported of the computer simulations on the magnetic behaviour of magnetic arrays of nanoscopic dots, placed in cells of the square lattice. We show that the remanence magnetization M(r) decreases with the array size. For arrays 50 x 50, we investigate also the stability of the magnetic structure of an array in an oscillating magnetic field. The damage spreading technique reveals that this stability increases with the standard deviation sigma of the switching field of individual elements of the array. On the other hand, M(r) decreases with sigma. An optimalization of the system (large M(r) and large stability) can then be reached at some intermediate value of sigma.