Voltage accuracy across shunt resistor
The tolerance of the resistor directly affects the voltage across it, all other things being equal. 

So at 20mA, a 0.1% error in resistance will affect the voltage across the resistor by 0.1%, which is 0.125% of span at 20mA (worst case). Span is 20mA - 4mA = 16mA. 

At 4mA it's 0.1% of 4mA, or 0.025% of span. 



Real current sources also have some output resistance (effectively in parallel) so there will be an effect for a non-zero (or differing from calibration value) load resistance. Usually that output resistance is positive so the voltage across the resistor is a bit less than would be otherwise expected. It is caused by the finite gain of the feedback loop. 

Both of those errors are added to whatever error is in the signal to begin with, and may increase or decrease the net error. Worst-case they make it worse, of course.