There is no such thing as 'non-inductive' any real component will have some inductance.

In the case of a current sense resistor, to add to Hero's post, the inductance of a current sense resistor will add to the measured voltage (at a different phase) across the resistor which you are trying to measure to calculate the current. This will be an error in your measurement. You can find out the voltage that will be developed due to the inductance of the part by V(t) = L * dI(t)/dt. The higher the inductance, the higher parasitic voltage. The higher the rate of change of current (directly linked to operating frequency), the higher the parasitic voltage. Parasitic capacitances will also cause ringing and if very severe, it could destroy the circuit, possibly the switching MOSFET or some other MOS part.