The Gaia SpectroPhotometric Standard Stars (SPSS) survey started in 2006, was awarded almost 450 observing nights and accumulated almost 100 000 raw data frames with both photometric and spectroscopic observations. Such large observational effort requires careful, homogeneous, and automatic data reduction and quality control procedures. In this paper, we quantitatively evaluate instrumental effects that might have a significant (i.e., ≥ 1 %) impact on the Gaia SPSS flux calibration. The measurements involve six different instruments, monitored over the eight years of observations dedicated to the Gaia flux standards campaigns: DOLORES@TNG in La Palma, EFOSC2@NTT and ROSS@REM in La Silla, CAFOS@2.2 m in Calar Alto, BFOSC@Cassini in Loiano, and LaRuca@1.5 m in San Pedro Mártir. We examine and quantitatively evaluate the following effects: CCD linearity and shutter times, calibration frames stability, lamp flexures, second order contamination, light polarization, and fringing. We present methods to correct for the relevant effects which can be applied to a wide range of observational projects at similar instruments.