What is the predictable difference of the voltage drop between the V+ and V- lines on a shunt resistor?
The only voltage drop you will see on V+ and V- sense lines will be due to the 2 front-end resistors you select for the differential amplifier configuration, multiplied by the input bias current of the op amp.

Checkout Table 7 of the datasheet:



Keep in mind that these will change part-to-part, and will depend on voltage, temperature, the resistor you select, etc.. 

Also keep in mind Note 2, which says this current is actually flowing OUT of the IC. Bias current can either be due to a current sink or source, and in this case it is a source inside the op-amp above the inputs.

The best way to reduce any error by this is selecting resistors in the 1k-10k range, no higher.