A number of aspects of magnetic force microscopy (MFM) specific to the imaging of hard magnetic films have been studied. Firstly, we show that topographic images made in tapping mode with probes characterized by the moderate cantilever stiffness usual for MFM (1--4 N/m), contain artifacts due to strong probe-sample interactions which lead to probe retraction. As a result, stiffer cantilevers (e.g. 40 N/m) are better adapted to characterizing such hard magnetic films. Secondly, imaging with probes coated by a hard magnetic film leads to phase maps which show a twofold symmetry, with paired dark/light contrast on opposite domain edges along the direction of the cantilever. This is due to the tilt of the direction of tip magnetizaiton and direction of oscillation, with respect to the sample normal. Thirdly, due to the long-range nature of the stray field produced by hard magnetic films containing micron-sized domains, MFM phase contrast reflects the stray field itself, as opposed to that of its spatial derivatives, as is generally the case in MFM.