The pitting corrosion of orthodontic apparatus elements in the oral environment is an interest of both clinicians and scientists dealing with the assessment of the biocompatibility of medical materials. This work presents a study on the effect of ready-to-use Listerine® and Meridol® mouthwashes and sodium fluoride on the resistance of the commercial Remanium®-type orthodontic archwire to pitting corrosion in artificial saliva at 37 °C. XRD, SEM, EDS, mechanical properties, and microhardness measurements were used to characterize the archwire. The in vitro corrosion resistance of the archwire was examined using the open-circuit potential method, electrochemical impedance spectroscopy, and anodic polarization curves. The physicochemical characteristics confirmed the presence of a bi-phase alloy with a mixed austenite/ferrite structure containing Fe 74.4(7) at.%, Cr 18.4(4) at.%, and Ni 7.2(4) at.%. The Fe–Cr–Ni alloy was characterized by high tensile strength and Vickers microhardness. EIS revealed the capacitive behavior with high corrosion resistance. It was found that the kinetics of pitting corrosion in the artificial saliva decreased in the presence of NaF and mouthwashes. The potentiodynamic characteristics confirmed the decrease in susceptibility to pitting corrosion after the modification of artificial saliva. The pitting corrosion mechanism of the self-passive oxide layer on the surface of the Fe–Cr–Ni electrode in the biological environment containing chloride ions was discussed in detail. Mechanical properties after corrosion tests were weakened.