In this paper, we propose using proton radiography to diagnose nonuniformity, in which a broad-energy-spectrum proton beam generated by an ultrashort, ultra-intense laser pulse is used to perform front and back radiography of a target, thereby enabling the diagnosis of nonuniformities and the determination of their longitudinal positions on the surfaces of, or within, the target. Using analytical formulas and our previously developed simplified model, we elucidate the main physical processes and the resulting phenomena in radiography, including Coulomb scattering leading to transverse resolution and fluence modulations on the detection plane, energy loss leading to energy spread and stopping in the target, and absorption of protons by nuclear reactions. Then we present the numerical results from Monte Carlo simulations of proton radiography of three nonuniform targets: tooth structures on the surface, embedded voids, and tooth structures covered with different material coatings. The target material is composed of C₁₀H₈O₄ and the coating is aluminum. The results show that proton scattering caused by target nonuniformity modulates the proton fluence distributions on the detection plane. When the proton energy is varied evidently, the modulation contrast is changed. When the target nonuniformity is located at a different longitudinal position, the modulation contrast may also change. Such a modulation and the difference in contrast between the front and back radiography enable the diagnosis of both the target nonuniformities and their longitudinal positions. When the thickness of the target is unknown or the nonuniform structures have different thicknesses, compared with fixed mono-energy proton radiography, protons in the medium energy range of the broad-energy-spectrum beam may produce higher contrast due to the nonuniformity of the target. For example, for a 200-μm-thick target with a 40-μm-thick tooth structure on its surface, the difference in contrast between the front and back radiography by a beam of protons with energy ranging from 5 to 6 MeV is 3.45%, while for a mono-energetic proton beam of 5 MeV, it is 2.56%. For a target with an embedded 40-μm-thick void, the difference in contrast between the front and back radiography changes from 0.79% to 2.68% when the displacement of the void center to the target center is changed from 20 μm to 80 μm in the longitudinal direction. These results demonstrate the advantages of using a broad-energy-spectrum proton beam and forward and back radiography in the diagnosis of target nonuniformities and their longitudinal positions.