A printer includes an ultraviolet (UV) curing device having UV light emitting diodes (LEDs) to cure UV curable inks ejected onto a surface after the surface travels past a plurality of printheads in the printer. A UV detector having UV sensors is positioned opposite the UV curing device so the UV sensors and UV LEDs are opposite one another in a one-to-one correspondence. A controller operates the UV curing device to direct UV light into the UV detector and receives electrical signals generated by the UV sensors. The controller compares these electrical signals to a predetermined threshold to identify defective LEDs in the UV curing device. The controller then determines how to move the UV curing device across the path of the surface to irradiate areas of the surface previously opposite the defective UV LEDs.