The current-induced destruction of superconductivity is discussed in wide superconducting thin films, whose width is greater than the magnetic field penetration depth, in weak magnetic fields. Particular attention is paid to the role of the boundary potential barrier (the Bin-Livingston barrier) in critical state formation and detection of the edge responsible for this critical state with different mutual orientations of external perpendicular magnetic field and transport current. Critical and resistive states of the film were visualized using the space-resolving low-temperature laser scanning microscopy (LTLSM) method, which enables detection of critical current-determining areas on the film edges. Based on these observations, a simple technique was developed for investigation of the critical state separately at each film edge, and for the estimation of residual magnetic fields in cryostats. The proposed method only requires recording of the current-voltage characteristics of the film in a weak magnetic field, thus circumventing the need for complex LTLSM techniques. Information thus obtained is particularly important for interpretation of studies of superconducting film single-photon light emission detectors.