Structural phase transitions in pyrochlore Cd2Nb2O7 were studied by means of single crystal x-ray scattering. On cooling below the ferroelastic transition at T1 = 204 K, the cubic Bragg peaks broaden in a manner consistent with weak orthorhombic distortion. The distortion evolves rather smoothly through the ferroelectric transition at T2 = 196 K, which explains the absence of sharp anomalies in the heat capacity and dielectric constant at this transition. At lower temperatures, the anomalous relaxor-like character of this compound is evident as a gradual reduction in the Bragg peak intensities, which continues down to the onset of another transition at T3 = 85 K. The studies of two Bragg peaks that are forbidden within the cubic phase reveal an interesting disparity: while the intensity for one of them increases in a classical mean-field manner below T1, the other shows unconventional behavior that is reminiscent of the pyrochlore superconductor Cd2Re2O7.