The morphological properties of YBCO superconducting films and their relationship to magnetic and transport phenomena are considered. A geometric probability analysis of the principal statistical characteristics of normal-phase clusters is performed, and their influence on the dynamics of trapped magnetic flux under the action of a pulsed transport current is revealed. The superconducting film is treated as a percolation system. It is found that the critical currents have a statistical distribution, which is specified by the morphology of the material being studied. The critical current for passage of the film into the resistive state is found.