Two universal effects in tunnel characteristics of layered metal—insulator—metal structures, where the dielectric barrier is formed by a nanoscale disordered oxide film, are discussed, namely: (1) a universal distribution of the layer transparencies, which does not depend on specific microscopic characteristics, and (2) the power-law change of the differential conductance of such heterostructures with an exponent value close to 1.33. Experimental results for superconducting three- and four-layered structures with inhomogeneous tunnel barriers are given and confirm the existence of a universal distribution of transparencies. Their simple theoretical interpretation based on the equipartition hypothesis of a product of the barrier height on the path, which is passed by an electron within the barrier, is given too. As shown, with increasing thickness of the defect-insulating layer, boson-assisted inelastic tunnelling becomes a dominant conduction mechanism resulting in the power-law differential conductance dependence on voltage with an exponent value, which characterizes the number of states localized inside the barrier and involved in the charge transfer through it. As shown for materials with a phonon density of states, which weakly depends on energy, the exponent value about 1.33 corresponds to hopping tunnelling conductance involving two defect states. Relevant experimental data for near-surface disordered dielectric layers in manganites are discussed in details.