Long range orientational and short range translational order is revealed by atomic force microscopy for the lattice of the hydrocarbon chains of Cd arachidate Langmuir-Blodgett films. This result is qualitatively in agreement with results previously obtained from integral measuring techniques. The local probe technique, however, also reveals the origin of this order : the short translational correlation length is due to local variations of the molecular density. It is not due to high densities of dislocations. The films do not represent hexatic phases which have been described in theories of two-dimensional melting processes. Tip/sample influences are also investigated in order to make sure that the mechanical scanning process does not disturb the specimen in an uncontrolled way. A systematic enlargement of the lattice is detected and explained with a simple model. A method to determine correct lattice constants from soft organic samples by atomic force microscopy is described. Previous studies where such artefacts have not been reported are discussed.