Complementary diffuse and inelastic synchrotron x-ray scattering measurements of lead zirconate-titanate single crystals with composition near the morphotropic phase boundary (x=0.475) are reported. In the temperature range 293 K<T<400 K a highly anisotropic quasielastic diffuse scattering is observed. Above 400 K this scattering disappears. Its main features can be reproduced by the model of inhomogeneous lattice deformations caused by inclusions of a tetragonal phase into a rhombohedral or monoclinic phase. This observation supports the idea that PZT at its morphotropic phase boundary is essentially structurally inhomogeneous.