Electrical noise can be induced into the wires, this causes false signaling to the controls. The risk is very low, in the speed pot input I have measured it and seen it as more flickering of the Hz display. Depending on the VFD there is some degree of noise filtering which can decrease the error/prevent it but depends on the level of noise induced in the wire and the sensitivity of the input/function being operated on. Short runs unshielded is not going to cause any issues, but depending on the type of electrical noise induced, there are different grounding schemas. Grounding and electrical noise is more complex and just not a simple solution, sometimes takes trial and error to find out what works best or to see that there is an issue. VFD's create a lot of RFI/EMI and this can be radiated like an antenna and also transmitted back through the input power.
One friend when he operated his lathe VFD, his wireless operated vacuum blast gates would turn on, another person tied the low level inputs with the motor cable had false signaling because the induced voltage into the signal wires. Phantom voltages are often a big problem with newer voltmeters, when measuring circuits where wires run in close proximity to other circuits, you shut one down and you will still measure an induced voltage from the other circuit, similar to how a transformer works. Typically the current is very low, in the old days they would use a light bulb to make sure the circuit wasn't hot, newer voltmeters have a LowZ setting which adds a lower resistance across the line when measuring the voltage. I also had a similar problem with an erratic tachometer when the VFD was running, grounding the shield wire at either or both ends made it worse. I floated the shield at both ends and it went away, noise can also got in through the DC power supply. There are different types of electrical filters and grounding techniques that can be used.
