One of the reasons that this is not a simple question is that there are several factors to take into consideration regarding the error margin for practical salinity measurements. Salinity itself is a derived measurement from temperature, conductivity, and pressure, so any errors in these sensors can propagate to salinity. For example, our initial accuracy specification for the SBE 3plus temperature sensor and SBE 4 conductivity sensor on an SBE 9plus CTD is approximately equivalent to an initial salinity accuracy of 0.003 PSU (note that conductivity units of mS/cm are roughly equivalent in terms of magnitude to PSU).
However, another issue to consider is that this accuracy is defined for a clean, well-mixed calibration bath. In the ocean, some of the biggest factors that impact salinity accuracy are 1) sensor drift from biofouling or surface oils for conductivity in particular and 2) dynamic errors that can occur on moving platforms, particularly when conditions are rapidly changing, which will be true for all sensors that measure salinity. Sea-Bird provides recommendations, design features such as a pumped flow path, and data processing routines to align and improve data for the salinity calculation to account for thermal transients and hysteresis, and to match sensor response times. Depending on the environment and the steepness of the gradient, and after careful data processing, this may continue to have an impact on salinity on the order of 0.002 PSU or more, for example. For more details, see Application Note 82.
Lastly, note that salinity in PSU is calculated according to the Practical Salinity Scale (PSS-78), which is defined as valid for salinity ranges from 2 – 42 PSU.