Magnetization reversal is investigated in the presence of anisotropy dispersion in weakly disordered CoxPd100-x(x=23,36,43) thin films. A fourfold in-plane magnetic anisotropy is observed for x=23, whereas an increase of the Co:Pd ratio induces a uniaxial anisotropy in x=36 and 43 films. Anomalous magnetization reversal appears along the hard axes (referred to as collapse of hard axes) in x=23 and 36 films, but disappears for x=43. The results are consistent with the two-grain Stoner-Wohlfarth model. It is argued that the collapse of the hard axes can be controlled by intergranular exchange interaction. Quadratic magneto-optical Kerr effect (QMOKE) is also observed in the films and is found to weaken if the in-plane anisotropy is lowered through the Co:Pd ratio. QMOKE is observed for magnetic field orientations near the hard axes but not exactly along it, in agreement with the two-grain Stoner-Wohlfarth model.