You have long runs of what appears to be unshielded un-twisted cables going to the pots?
Each cable to each pot would be best as shielded (shield to gnd) cables with the groung connected only at Arduino end - dont connect it to the chassis at the pot end. You should try something like microphone cable with two shielded conductors, one for 5V and one for the wiper)
You pots should not be high impedance, try 2k to 10k or so, 100k would be too high