The intensity flatness and wavefront shape in a coherent hard-x-ray beam totally reflected by flat mirrors that have surface bumps modeled by Gaussian functions were investigated by use of a wave-optical simulation code. Simulated results revealed the necessity for peak-to-valley height accuracy of better than 1 nm at a lateral resolution near 0.1 mm to remove high-contrast interference fringes and appreciable wavefront phase errors. Three mirrors that had different surface qualities were tested at the 1 km-long beam line at the SPring-8/Japan Synchrotron Radiation Research Institute. Interference fringes faded when the surface figure was corrected below the subnanometer level to a spatial resolution close to 0.1 mm, as indicated by the simulated results.