Do carbon film resistors have any effect on AC?
There is inductance and there is capacitance between the spiral turns and from end-to-end. It's generally not important until you get to VHF frequencies, but of course the effect is relatively larger on higher resistances for the capacitance and the inductance effect is relatively higher on very low resistances. 

For example, if you use this calculator, a coil with 8 turns 2mm diameter and 7mm long would have an inductance of 0.04uH, so at 100MHz and Xl/R = 0.1, R &lt; 250\$\Omega\$. Note that if you have a current sense resistor of very low value, even a fraction of a microhenry inductance will start to have a noticeable effect at moderate frequencies. A 10m\$\Omega\$ resistor with 40nH inductance would be affected similarly at only 4kHz. 

Parasitic capacitance works similarly from the other end of the frequency scale- a 10M\$\Omega\$ resistor with 0.4 pF of end-to-end capacitance would be be affected similarly at only 4kHz.