How to acquire current values in data acquisiton accurately when using a shunt resistor in a current loop?
At 20 mA the resistor will be dissipating more power than at 4 mA. Say the resistor is 250 ohm (as per your previous question How to achieve common ground for a single ended input?), the power will be 100 mW at 20mA whereas at 4 mA the power will only be 4 mW.

If your resistor warms up 10 ºC and is a 25ppm/ºC type the resistance change will be from 250 ohm to 250.06 ohms or down to 249.94 ohms.

If your resistor warms up 20 ºC and it is a 50ppm/ºC type the resistance will change from 250 ohm to 250.25 ohms or down to 249.75 ohms.

This seems around the same order as what you are measuring. I calculate a change in resistance of 0.47 ohms - could this be due to self-heating?